diff --git a/Project.toml b/Project.toml
index 12d3aab9d..fce114b23 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "LinearSolve"
 uuid = "7ed4a6bd-45f5-4d41-b270-4a48e9bafcae"
 authors = ["SciML"]
-version = "2.20.0"
+version = "2.20.1"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
@@ -26,6 +26,7 @@ SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
 Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Sparspak = "e56a9233-b9d6-4f03-8d0f-1825330902ac"
+StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
 
 [weakdeps]
@@ -48,6 +49,7 @@ LinearSolveBandedMatricesExt = "BandedMatrices"
 LinearSolveBlockDiagonalsExt = "BlockDiagonals"
 LinearSolveCUDAExt = "CUDA"
 LinearSolveEnzymeExt = ["Enzyme", "EnzymeCore"]
+LinearSolveFastAlmostBandedMatricesExt = ["FastAlmostBandedMatrices"]
 LinearSolveHYPREExt = "HYPRE"
 LinearSolveIterativeSolversExt = "IterativeSolvers"
 LinearSolveKernelAbstractionsExt = "KernelAbstractions"
@@ -55,7 +57,6 @@ LinearSolveKrylovKitExt = "KrylovKit"
 LinearSolveMetalExt = "Metal"
 LinearSolvePardisoExt = "Pardiso"
 LinearSolveRecursiveArrayToolsExt = "RecursiveArrayTools"
-LinearSolveFastAlmostBandedMatricesExt = ["FastAlmostBandedMatrices"]
 
 [compat]
 Aqua = "0.8"
@@ -101,6 +102,8 @@ SciMLOperators = "0.3"
 Setfield = "1"
 SparseArrays = "1.9"
 Sparspak = "0.3.6"
+StaticArraysCore = "1"
+StaticArrays = "1"
 Test = "1"
 UnPack = "1"
 julia = "1.9"
@@ -126,7 +129,8 @@ Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Aqua", "Test", "IterativeSolvers", "InteractiveUtils", "JET", "KrylovKit", "Pkg", "Random", "SafeTestsets", "MultiFloats", "ForwardDiff", "HYPRE", "MPI", "BlockDiagonals", "Enzyme", "FiniteDiff", "BandedMatrices", "FastAlmostBandedMatrices"]
+test = ["Aqua", "Test", "IterativeSolvers", "InteractiveUtils", "JET", "KrylovKit", "Pkg", "Random", "SafeTestsets", "MultiFloats", "ForwardDiff", "HYPRE", "MPI", "BlockDiagonals", "Enzyme", "FiniteDiff", "BandedMatrices", "FastAlmostBandedMatrices", "StaticArrays"]
diff --git a/src/LinearSolve.jl b/src/LinearSolve.jl
index 2d586547f..572e310e9 100644
--- a/src/LinearSolve.jl
+++ b/src/LinearSolve.jl
@@ -26,6 +26,8 @@ PrecompileTools.@recompile_invalidations begin
     using Requires
     import InteractiveUtils
 
+    import StaticArraysCore: StaticArray, SVector, MVector, SMatrix, MMatrix
+
     using LinearAlgebra: BlasInt, LU
     using LinearAlgebra.LAPACK: require_one_based_indexing,
         chkfinite, chkstride1,
diff --git a/src/default.jl b/src/default.jl
index 574d81885..231f81361 100644
--- a/src/default.jl
+++ b/src/default.jl
@@ -175,6 +175,10 @@ function defaultalg(A, b, assump::OperatorAssumptions)
                 DefaultAlgorithmChoice.LUFactorization
             end
 
+            # For static arrays GMRES allocates a lot. Use factorization
+        elseif A isa StaticArray
+            DefaultAlgorithmChoice.LUFactorization
+
             # This catches the cases where a factorization overload could exist
             # For example, BlockBandedMatrix
         elseif A !== nothing && ArrayInterface.isstructured(A)
@@ -186,6 +190,9 @@ function defaultalg(A, b, assump::OperatorAssumptions)
         end
     elseif assump.condition === OperatorCondition.WellConditioned
         DefaultAlgorithmChoice.NormalCholeskyFactorization
+    elseif A isa StaticArray
+        # Static Array doesn't have QR() \ b defined
+        DefaultAlgorithmChoice.SVDFactorization
     elseif assump.condition === OperatorCondition.IllConditioned
         if is_underdetermined(A)
             # Underdetermined
diff --git a/src/factorization.jl b/src/factorization.jl
index ec3fad4fd..e6476eb9d 100644
--- a/src/factorization.jl
+++ b/src/factorization.jl
@@ -10,6 +10,10 @@ end
 
 _ldiv!(x, A, b) = ldiv!(x, A, b)
 
+_ldiv!(x, A, b::SVector) = (x .= A \ b)
+_ldiv!(::SVector, A, b::SVector) = (A \ b)
+_ldiv!(::SVector, A, b) = (A \ b)
+
 function _ldiv!(x::Vector, A::Factorization, b::Vector)
     # workaround https://github.com/JuliaLang/julia/issues/43507
     # Fallback if working with non-square matrices
@@ -74,6 +78,8 @@ function do_factorization(alg::LUFactorization, A, b, u)
     if A isa AbstractSparseMatrixCSC
         return lu(SparseMatrixCSC(size(A)..., getcolptr(A), rowvals(A), nonzeros(A)),
             check = false)
+    elseif !ArrayInterface.can_setindex(typeof(A))
+        fact = lu(A, alg.pivot, check = false)
     else
         fact = lu!(A, alg.pivot, check = false)
     end
@@ -136,10 +142,14 @@ end
 
 function do_factorization(alg::QRFactorization, A, b, u)
     A = convert(AbstractMatrix, A)
-    if alg.inplace && !(A isa SparseMatrixCSC) && !(A isa GPUArraysCore.AbstractGPUArray)
-        fact = qr!(A, alg.pivot)
+    if ArrayInterface.can_setindex(typeof(A))
+        if alg.inplace && !(A isa SparseMatrixCSC) && !(A isa GPUArraysCore.AbstractGPUArray)
+            fact = qr!(A, alg.pivot)
+        else
+            fact = qr(A) # CUDA.jl does not allow other args!
+        end
     else
-        fact = qr(A) # CUDA.jl does not allow other args!
+        fact = qr(A, alg.pivot)
     end
     return fact
 end
@@ -202,6 +212,16 @@ function do_factorization(alg::CholeskyFactorization, A, b, u)
     return fact
 end
 
+function init_cacheval(alg::CholeskyFactorization, A::SMatrix{S1, S2}, b, u, Pl, Pr,
+    maxiters::Int, abstol, reltol, verbose::Bool,
+    assumptions::OperatorAssumptions) where {S1, S2}
+    # StaticArrays doesn't have the pivot argument. Prevent generic fallback.
+    # CholeskyFactorization is part of DefaultLinearSolver, so it is possible that `A` is
+    # not Hermitian.
+    (!issquare(A) || !ishermitian(A)) && return nothing
+    cholesky(A)
+end
+
 function init_cacheval(alg::CholeskyFactorization, A, b, u, Pl, Pr,
     maxiters::Int, abstol, reltol, verbose::Bool,
     assumptions::OperatorAssumptions)
@@ -276,11 +296,15 @@ SVDFactorization() = SVDFactorization(false, LinearAlgebra.DivideAndConquer())
 
 function do_factorization(alg::SVDFactorization, A, b, u)
     A = convert(AbstractMatrix, A)
-    fact = svd!(A; full = alg.full, alg = alg.alg)
+    if ArrayInterface.can_setindex(typeof(A))
+        fact = svd!(A; alg.full, alg.alg)
+    else
+        fact = svd(A; alg.full)
+    end
     return fact
 end
 
-function init_cacheval(alg::SVDFactorization, A::Matrix, b, u, Pl, Pr,
+function init_cacheval(alg::SVDFactorization, A::Union{Matrix, SMatrix}, b, u, Pl, Pr,
     maxiters::Int, abstol, reltol, verbose::Bool,
     assumptions::OperatorAssumptions)
     ArrayInterface.svd_instance(convert(AbstractMatrix, A))
@@ -882,7 +906,8 @@ end
 function init_cacheval(alg::NormalCholeskyFactorization, A, b, u, Pl, Pr,
     maxiters::Int, abstol, reltol, verbose::Bool,
     assumptions::OperatorAssumptions)
-    ArrayInterface.cholesky_instance(convert(AbstractMatrix, A), alg.pivot)
+    A_ = convert(AbstractMatrix, A)
+    ArrayInterface.cholesky_instance(Symmetric((A)' * A, :L), alg.pivot)
 end
 
 function init_cacheval(alg::NormalCholeskyFactorization,
@@ -1128,6 +1153,11 @@ function init_cacheval(::SparspakFactorization, A, b, u, Pl, Pr, maxiters::Int,
     end
 end
 
+function init_cacheval(::SparspakFactorization, ::StaticArray, b, u, Pl, Pr,
+    maxiters::Int, abstol, reltol, verbose::Bool, assumptions::OperatorAssumptions)
+    nothing
+end
+
 function SciMLBase.solve!(cache::LinearCache, alg::SparspakFactorization; kwargs...)
     A = cache.A
     if cache.isfresh
diff --git a/test/default_algs.jl b/test/default_algs.jl
index 3435b2f19..431e2d155 100644
--- a/test/default_algs.jl
+++ b/test/default_algs.jl
@@ -50,7 +50,7 @@ solve(prob)
     A = rand(4, 4)
     b = rand(4)
     prob = LinearProblem(A, b)
-    JET.@test_opt init(prob, nothing)
+    VERSION ≥ v"1.10-" && JET.@test_opt init(prob, nothing)
     JET.@test_opt solve(prob, LUFactorization())
     JET.@test_opt solve(prob, GenericLUFactorization())
     @test_skip JET.@test_opt solve(prob, QRFactorization())
diff --git a/test/runtests.jl b/test/runtests.jl
index 67fc2626d..ae12f0544 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -17,6 +17,7 @@ if GROUP == "All" || GROUP == "Core"
     @time @safetestset "Enzyme Derivative Rules" include("enzyme.jl")
     @time @safetestset "Traits" include("traits.jl")
     @time @safetestset "BandedMatrices" include("banded.jl")
+    @time @safetestset "Static Arrays" include("static_arrays.jl")
 end
 
 if GROUP == "LinearSolveCUDA"
diff --git a/test/static_arrays.jl b/test/static_arrays.jl
new file mode 100644
index 000000000..5c6ccf252
--- /dev/null
+++ b/test/static_arrays.jl
@@ -0,0 +1,24 @@
+using LinearSolve, StaticArrays, LinearAlgebra
+
+A = SMatrix{5, 5}(Hermitian(rand(5, 5) + I))
+b = SVector{5}(rand(5))
+
+for alg in (nothing, LUFactorization(), SVDFactorization(), CholeskyFactorization(),
+    KrylovJL_GMRES())
+    sol = solve(LinearProblem(A, b), alg)
+    @test norm(A * sol .- b) < 1e-10
+end
+
+A = SMatrix{7, 5}(rand(7, 5))
+b = SVector{7}(rand(7))
+
+for alg in (nothing, SVDFactorization(), KrylovJL_LSMR())
+    @test_nowarn solve(LinearProblem(A, b), alg)
+end
+
+A = SMatrix{5, 7}(rand(5, 7))
+b = SVector{5}(rand(5))
+
+for alg in (nothing, SVDFactorization(), KrylovJL_LSMR())
+    @test_nowarn solve(LinearProblem(A, b), alg)
+end