diff --git a/ext/StaticArraysExt.jl b/ext/StaticArraysExt.jl
new file mode 100644
index 0000000000..7887a2244b
--- /dev/null
+++ b/ext/StaticArraysExt.jl
@@ -0,0 +1,14 @@
+# compatibility with StaticArrays
+
+module StaticArraysExt
+
+using ..CUDA
+using ..CUDA: @device_override, @print_and_throw
+
+import StaticArrays
+
+# same quirk as for some Base methods in src/device/quirks.jl
+@device_override @noinline StaticArrays.dimension_mismatch_fail(::Type{SA}, a::AbstractArray) where {SA<:StaticArrays.StaticArray} =
+    @print_and_throw("DimensionMismatch while trying to convert to StaticArray: Expected and actual length of input array differ.")
+
+end  # extension module
\ No newline at end of file
diff --git a/src/CUDA.jl b/src/CUDA.jl
index bd539273ff..1fb628f0f9 100644
--- a/src/CUDA.jl
+++ b/src/CUDA.jl
@@ -122,6 +122,9 @@ include("CUDAKernels.jl")
 import .CUDAKernels: CUDABackend
 export CUDABackend
 
+# StaticArrays is still a direct dependency, so directly include the extension
+include("../ext/StaticArraysExt.jl")
+
 include("precompile.jl")
 
 end
diff --git a/test/libraries/staticarrays.jl b/test/libraries/staticarrays.jl
new file mode 100644
index 0000000000..98f1435c0d
--- /dev/null
+++ b/test/libraries/staticarrays.jl
@@ -0,0 +1,30 @@
+using LinearAlgebra: mul!
+using StaticArrays
+
+@testset "StaticArrays" begin
+    function batched_matvec(ms::CuArray, vs::CuArray)
+        function matvec_kernel(out, ms, vs, ::Val{N}, ::Val{M}) where {N, M}
+            i = (blockIdx().x - 1) * blockDim().x + threadIdx().x
+            # Call constructors without @inbounds.
+            # This asserts that the @device_override
+            # for StaticArrays.dimension_mismatch_fail() works.
+            m = SMatrix{N, M, Float32}(@view ms[:, :, i])
+            v = SVector{M, Float32}(@view vs[:, i])
+            out[:, i] .= m * v
+            nothing
+        end
+
+        out = similar(ms, (size(ms, 1), size(ms, 3)))
+        @cuda threads=size(ms, 3) matvec_kernel(out, ms, vs, Val(size(ms, 1)), Val(size(ms, 2)))
+        out
+    end
+
+    function batched_matvec(ms, vs)
+        out = similar(ms, (size(ms, 1), size(ms, 3)))
+        foreach((o, m, v) -> mul!(o, m, v), eachcol(out), eachslice(ms; dims=3), eachcol(vs))
+        out
+    end
+
+    ms, vs = randn(Float32, 3, 2, 4), randn(Float32, 2, 4)
+    @test batched_matvec(ms, vs) ≈ Array(batched_matvec(cu(ms), cu(vs)))
+end
\ No newline at end of file