diff --git a/src/FillArrays.jl b/src/FillArrays.jl
index 60c22c33..3222a8f7 100644
--- a/src/FillArrays.jl
+++ b/src/FillArrays.jl
@@ -10,7 +10,7 @@ import Base: size, getindex, setindex!, IndexStyle, checkbounds, convert,
 
 import LinearAlgebra: rank, svdvals!, tril, triu, tril!, triu!, diag, transpose, adjoint, fill!,
     dot, norm2, norm1, normInf, normMinusInf, normp, lmul!, rmul!, diagzero, AdjointAbsVec, TransposeAbsVec,
-    issymmetric, ishermitian, AdjOrTransAbsVec, checksquare, mul!
+    issymmetric, ishermitian, AdjOrTransAbsVec, checksquare, mul!, kron
 
 
 import Base.Broadcast: broadcasted, DefaultArrayStyle, broadcast_shape
@@ -411,6 +411,7 @@ Base.replace_in_print_matrix(A::RectDiagonal, i::Integer, j::Integer, s::Abstrac
 
 
 const RectOrDiagonal{T,V,Axes} = Union{RectDiagonal{T,V,Axes}, Diagonal{T,V}}
+const RectDiagonalEye{T} = RectDiagonal{T,<:Ones{T,1}}
 const SquareEye{T,Axes} = Diagonal{T,Ones{T,1,Tuple{Axes}}}
 const Eye{T,Axes} = RectOrDiagonal{T,Ones{T,1,Tuple{Axes}}}
 
diff --git a/src/fillalgebra.jl b/src/fillalgebra.jl
index 3dd222c3..6d5c8394 100644
--- a/src/fillalgebra.jl
+++ b/src/fillalgebra.jl
@@ -434,3 +434,23 @@ fillzero(::Type{Zeros{T,N,AXIS}}, n, m) where {T,N,AXIS} = Zeros{T,N,AXIS}((n, m
 fillzero(::Type{F}, n, m) where F = throw(ArgumentError("Cannot create a zero array of type $F"))
 
 diagzero(D::Diagonal{F}, i, j) where F<:AbstractFill = fillzero(F, axes(D.diag[i], 1), axes(D.diag[j], 2))
+
+# kron
+
+_kronsize(f::AbstractFillVector, g::AbstractFillVector) = (size(f,1)*size(g,1),)
+_kronsize(f::AbstractFillVecOrMat, g::AbstractFillVecOrMat) = (size(f,1)*size(g,1), size(f,2)*size(g,2))
+function _kron(f::AbstractFill, g::AbstractFill, sz)
+    v = getindex_value(f)*getindex_value(g)
+    Fill(v, sz)
+end
+function _kron(f::Zeros, g::Zeros, sz)
+    Zeros{promote_type(eltype(f), eltype(g))}(sz)
+end
+function _kron(f::Ones, g::Ones, sz)
+    Ones{promote_type(eltype(f), eltype(g))}(sz)
+end
+function kron(f::AbstractFillVecOrMat, g::AbstractFillVecOrMat)
+    sz = _kronsize(f, g)
+    _kron(f, g, sz)
+end
+kron(E1::RectDiagonalEye, E2::RectDiagonalEye) = kron(sparse(E1), sparse(E2))
diff --git a/test/runtests.jl b/test/runtests.jl
index f28f64bd..1ffd2d5a 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1489,6 +1489,53 @@ end
     end
 end
 
+@testset "kron" begin
+    for T in (Fill, Zeros, Ones), sz in ((2,), (2,2))
+        f = T{Int}((T == Fill ? (3,sz...) : sz)...)
+        g = Ones{Int}(2)
+        z = Zeros{Int}(2)
+        fc = collect(f)
+        gc = collect(g)
+        zc = collect(z)
+        @test kron(f, f) == kron(fc, fc)
+        @test kron(f, f) isa T{Int,length(sz)}
+        @test kron(f, g) == kron(fc, gc)
+        @test kron(f, g) isa AbstractFill{Int,length(sz)}
+        @test kron(g, f) == kron(gc, fc)
+        @test kron(g, f) isa AbstractFill{Int,length(sz)}
+        @test kron(f, z) == kron(fc, zc)
+        @test kron(f, z) isa AbstractFill{Int,length(sz)}
+        @test kron(z, f) == kron(zc, fc)
+        @test kron(z, f) isa AbstractFill{Int,length(sz)}
+        @test kron(f, f .+ 0.5) == kron(fc, fc .+ 0.5)
+        @test kron(f, f .+ 0.5) isa AbstractFill{Float64,length(sz)}
+        @test kron(f, g .+ 0.5) isa AbstractFill{Float64,length(sz)}
+    end
+
+    for m in (Fill(2,2,2), "a"), sz in ((2,2), (2,))
+        f = Fill(m, sz)
+        g = fill(m, sz)
+        @test kron(f, f) == kron(g, g)
+    end
+
+    @test_throws MethodError kron(Fill("a",2), Zeros(1)) # can't multiply String and Float64
+
+    E = Eye(2)
+    K = kron(E, E)
+    @test K isa Diagonal
+    if VERSION >= v"1.9"
+        @test K isa typeof(E)
+    end
+    C = collect(E)
+    @test K == kron(C, C)
+
+    E = Eye(2,3)
+    K = kron(E, E)
+    C = collect(E)
+    @test K == kron(C, C)
+    @test issparse(kron(E,E))
+end
+
 @testset "dot products" begin
     n = 15
     o = Ones(1:n)