diff --git a/Project.toml b/Project.toml
index 28518343..091a37f9 100644
--- a/Project.toml
+++ b/Project.toml
@@ -10,10 +10,12 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
 
 [weakdeps]
+LoopVectorization = "bdcacae8-1622-11e9-2a5c-532679323890"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
 
 [extensions]
+SciMLOperatorsLoopVectorizationExt = "LoopVectorization"
 SciMLOperatorsSparseArraysExt = "SparseArrays"
 SciMLOperatorsStaticArraysCoreExt = "StaticArraysCore"
 
@@ -22,6 +24,7 @@ Accessors = "0.1.42"
 ArrayInterface = "7.19"
 DocStringExtensions = "0.9.4"
 LinearAlgebra = "1.10"
+LoopVectorization = "0.12"
 SparseArrays = "1.10"
 StaticArraysCore = "1"
 julia = "1.10"
diff --git a/ext/SciMLOperatorsLoopVectorizationExt.jl b/ext/SciMLOperatorsLoopVectorizationExt.jl
new file mode 100644
index 00000000..343c7240
--- /dev/null
+++ b/ext/SciMLOperatorsLoopVectorizationExt.jl
@@ -0,0 +1,46 @@
+module SciMLOperatorsLoopVectorizationExt
+
+import LoopVectorization: @turbo
+import SciMLOperators
+
+const StridedMatrixOperator = SciMLOperators.MatrixOperator{<:Any, <:StridedMatrix}
+
+SciMLOperators._has_tensor_outer_mul_fast(::StridedMatrixOperator) = true
+
+function SciMLOperators._tensor_outer_mul_fast!(
+        w, outer::StridedMatrixOperator, C, mi::Int, mo::Int, no::Int, k::Int
+    )
+    A = outer.A
+    C = reshape(C, (mi, no, k))
+    W = reshape(w, (mi, mo, k))
+
+    @turbo for j in 1:k, m in 1:mo, i in 1:mi
+        acc = zero(eltype(w))
+        for o in 1:no
+            acc += A[m, o] * C[i, o, j]
+        end
+        W[i, m, j] = acc
+    end
+
+    return w
+end
+
+function SciMLOperators._tensor_outer_mul_fast!(
+        w, outer::StridedMatrixOperator, C, mi::Int, mo::Int, no::Int, k::Int, α, β
+    )
+    A = outer.A
+    C = reshape(C, (mi, no, k))
+    W = reshape(w, (mi, mo, k))
+
+    @turbo for j in 1:k, m in 1:mo, i in 1:mi
+        acc = zero(eltype(w))
+        for o in 1:no
+            acc += A[m, o] * C[i, o, j]
+        end
+        W[i, m, j] = α * acc + β * W[i, m, j]
+    end
+
+    return w
+end
+
+end
diff --git a/src/tensor.jl b/src/tensor.jl
index 50089bf0..11f144b6 100644
--- a/src/tensor.jl
+++ b/src/tensor.jl
@@ -413,6 +413,9 @@ end
 # helper functions
 const PERM = (2, 1, 3)
 
+_has_tensor_outer_mul_fast(outer) = false
+function _tensor_outer_mul_fast! end
+
 function outer_mul(L::TensorProductOperator, v::AbstractVecOrMat, C::AbstractVecOrMat)
     outer, inner = L.ops
 
@@ -465,6 +468,11 @@ function outer_mul!(w::AbstractVecOrMat, L::TensorProductOperator, v::AbstractVe
         return w
     end
 
+    if _has_tensor_outer_mul_fast(outer)
+        _tensor_outer_mul_fast!(w, outer, C1, mi, mo, no, k)
+        return w
+    end
+
     C2, C3 = L.cache[2:3]
 
     C1 = reshape(C1, (mi, no, k))
@@ -503,6 +511,11 @@ function outer_mul!(
         return w
     end
 
+    if _has_tensor_outer_mul_fast(outer)
+        _tensor_outer_mul_fast!(w, outer, v, mi, mo, no, k, α, β)
+        return w
+    end
+
     C2, C3, c4 = L.cache[2:4]
 
     C = reshape(v, (mi, no, k))
diff --git a/test/Project.toml b/test/Project.toml
index 342ab975..8d16f7b1 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,6 +1,7 @@
 [deps]
 FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+LoopVectorization = "bdcacae8-1622-11e9-2a5c-532679323890"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
@@ -10,5 +11,6 @@ Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [compat]
 FFTW = "1.10.0"
+LoopVectorization = "0.12"
 SafeTestsets = "0.1.0"
 Zygote = "0.7.10"
diff --git a/test/matrix.jl b/test/matrix.jl
index 3d363e56..355b1f36 100644
--- a/test/matrix.jl
+++ b/test/matrix.jl
@@ -2,6 +2,7 @@ using SciMLOperators, LinearAlgebra
 using SparseArrays
 using Random
 using Test
+using LoopVectorization
 
 using SciMLOperators: InvertibleOperator, InvertedOperator, ⊗, AbstractSciMLOperator
 using FFTW