diff --git a/src/bidiag.jl b/src/bidiag.jl
index 19a80336..13439ff9 100644
--- a/src/bidiag.jl
+++ b/src/bidiag.jl
@@ -178,6 +178,19 @@ end
     return A
 end
 
+@inline function setindex!(A::Bidiagonal, x, b::BandIndex)
+    @boundscheck checkbounds(A, b)
+    if b.band == 0
+        @inbounds A.dv[b.index] = x
+    elseif b.band ∈ (-1,1) && b.band == _offdiagind(A.uplo)
+        @inbounds A.ev[b.index] = x
+    elseif !iszero(x)
+        throw(ArgumentError(LazyString(lazy"cannot set entry $(to_indices(A, (b,))) off the ",
+            A.uplo == 'U' ? "upper" : "lower", " bidiagonal band to a nonzero value ", x)))
+    end
+    return A
+end
+
 Base._reverse(A::Bidiagonal, dims) = reverse!(Matrix(A); dims)
 Base._reverse(A::Bidiagonal, ::Colon) = Bidiagonal(reverse(A.dv), reverse(A.ev), A.uplo == 'U' ? :L : :U)
 
diff --git a/src/diagonal.jl b/src/diagonal.jl
index 10b8e7b0..3f72c16c 100644
--- a/src/diagonal.jl
+++ b/src/diagonal.jl
@@ -218,7 +218,7 @@ zeroslike(::Type{M}, sz::Tuple{Integer, Vararg{Integer}}) where {M<:AbstractMatr
     r
 end
 
-function setindex!(D::Diagonal, v, i::Int, j::Int)
+@inline function setindex!(D::Diagonal, v, i::Int, j::Int)
     @boundscheck checkbounds(D, i, j)
     if i == j
         @inbounds D.diag[i] = v
@@ -228,6 +228,15 @@ function setindex!(D::Diagonal, v, i::Int, j::Int)
     return D
 end
 
+@inline function setindex!(D::Diagonal, v, b::BandIndex)
+    @boundscheck checkbounds(D, b)
+    if b.band == 0
+        @inbounds D.diag[b.index] = v
+    elseif !iszero(v)
+        throw(ArgumentError(lazy"cannot set off-diagonal entry $(to_indices(D, (b,))) to a nonzero value ($v)"))
+    end
+    return D
+end
 
 ## structured matrix methods ##
 function Base.replace_in_print_matrix(A::Diagonal,i::Integer,j::Integer,s::AbstractString)
diff --git a/src/tridiag.jl b/src/tridiag.jl
index 808f5cc8..c2290104 100644
--- a/src/tridiag.jl
+++ b/src/tridiag.jl
@@ -508,6 +508,17 @@ Base._reverse!(A::SymTridiagonal, dims::Colon) = (reverse!(A.dv); reverse!(A.ev)
     return A
 end
 
+@inline function setindex!(A::SymTridiagonal, x, b::BandIndex)
+    @boundscheck checkbounds(A, b)
+    if b.band == 0
+        issymmetric(x) || throw(ArgumentError("cannot set a diagonal entry of a SymTridiagonal to an asymmetric value"))
+        @inbounds A.dv[b.index] = x
+    else
+        throw(ArgumentError(lazy"cannot set off-diagonal entry $(to_indices(A, (b,)))"))
+    end
+    return A
+end
+
 ## Tridiagonal matrices ##
 struct Tridiagonal{T,V<:AbstractVector{T}} <: AbstractMatrix{T}
     dl::V    # sub-diagonal
@@ -775,6 +786,21 @@ end
     return A
 end
 
+@inline function setindex!(A::Tridiagonal, x, b::BandIndex)
+    @boundscheck checkbounds(A, b)
+    if b.band == 0
+        @inbounds A.d[b.index] = x
+    elseif b.band == -1
+        @inbounds A.dl[b.index] = x
+    elseif b.band == 1
+        @inbounds A.du[b.index] = x
+    elseif !iszero(x)
+        throw(ArgumentError(LazyString(lazy"cannot set entry $(to_indices(A, (b,))) off ",
+            lazy"the tridiagonal band to a nonzero value ($x)")))
+    end
+    return A
+end
+
 ## structured matrix methods ##
 function Base.replace_in_print_matrix(A::Tridiagonal,i::Integer,j::Integer,s::AbstractString)
     i==j-1||i==j||i==j+1 ? s : Base.replace_with_centered_mark(s)
diff --git a/test/bidiag.jl b/test/bidiag.jl
index 2488cd3f..fcd9de77 100644
--- a/test/bidiag.jl
+++ b/test/bidiag.jl
@@ -1205,4 +1205,21 @@ end
     @test rmul!(B, D) == B2
 end
 
+@testset "setindex! with BandIndex" begin
+    B = Bidiagonal(zeros(3), zeros(2), :U)
+    B[LinearAlgebra.BandIndex(0,2)] = 1
+    @test B[2,2] == 1
+    B[LinearAlgebra.BandIndex(1,1)] = 2
+    @test B[1,2] == 2
+    @test_throws "cannot set entry $((1,3)) off the upper bidiagonal band" B[LinearAlgebra.BandIndex(2,1)] = 2
+
+    B = Bidiagonal(zeros(3), zeros(2), :L)
+    B[LinearAlgebra.BandIndex(-1,1)] = 2
+    @test B[2,1] == 2
+    @test_throws "cannot set entry $((3,1)) off the lower bidiagonal band" B[LinearAlgebra.BandIndex(-2,1)] = 2
+
+    @test_throws BoundsError B[LinearAlgebra.BandIndex(size(B,1),1)]
+    @test_throws BoundsError B[LinearAlgebra.BandIndex(0,size(B,1)+1)]
+end
+
 end # module TestBidiagonal
diff --git a/test/diagonal.jl b/test/diagonal.jl
index cbd9edb4..207e52d9 100644
--- a/test/diagonal.jl
+++ b/test/diagonal.jl
@@ -1489,4 +1489,13 @@ end
     @test !isreal(im*D)
 end
 
+@testset "setindex! with BandIndex" begin
+    D = Diagonal(zeros(2))
+    D[LinearAlgebra.BandIndex(0,2)] = 1
+    @test D[2,2] == 1
+    @test_throws "cannot set off-diagonal entry $((1,2))" D[LinearAlgebra.BandIndex(1,1)] = 1
+    @test_throws BoundsError D[LinearAlgebra.BandIndex(size(D,1),1)]
+    @test_throws BoundsError D[LinearAlgebra.BandIndex(0,size(D,1)+1)]
+end
+
 end # module TestDiagonal
diff --git a/test/tridiag.jl b/test/tridiag.jl
index 849dfa17..115b7ab2 100644
--- a/test/tridiag.jl
+++ b/test/tridiag.jl
@@ -1184,4 +1184,27 @@ end
     @test convert(SymTridiagonal, S) == S
 end
 
+@testset "setindex! with BandIndex" begin
+    T = Tridiagonal(zeros(3), zeros(4), zeros(3))
+    T[LinearAlgebra.BandIndex(0,2)] = 1
+    @test T[2,2] == 1
+    T[LinearAlgebra.BandIndex(1,2)] = 2
+    @test T[2,3] == 2
+    T[LinearAlgebra.BandIndex(-1,2)] = 3
+    @test T[3,2] == 3
+
+    @test_throws "cannot set entry $((1,3)) off the tridiagonal band" T[LinearAlgebra.BandIndex(2,1)] = 1
+    @test_throws "cannot set entry $((3,1)) off the tridiagonal band" T[LinearAlgebra.BandIndex(-2,1)] = 1
+    @test_throws BoundsError T[LinearAlgebra.BandIndex(size(T,1),1)]
+    @test_throws BoundsError T[LinearAlgebra.BandIndex(0,size(T,1)+1)]
+
+    S = SymTridiagonal(zeros(4), zeros(3))
+    S[LinearAlgebra.BandIndex(0,2)] = 1
+    @test S[2,2] == 1
+
+    @test_throws "cannot set off-diagonal entry $((1,3))" S[LinearAlgebra.BandIndex(2,1)] = 1
+    @test_throws BoundsError S[LinearAlgebra.BandIndex(size(S,1),1)]
+    @test_throws BoundsError S[LinearAlgebra.BandIndex(0,size(S,1)+1)]
+end
+
 end # module TestTridiagonal