diff --git a/base/div.jl b/base/div.jl
index 82234a32ff9cf..68b020e93ef5d 100644
--- a/base/div.jl
+++ b/base/div.jl
@@ -114,6 +114,8 @@ rem(x, y, r::RoundingMode)
 rem(x, y, ::RoundingMode{:ToZero}) = rem(x, y)
 rem(x, y, ::RoundingMode{:Down}) = mod(x, y)
 rem(x, y, ::RoundingMode{:Up}) = mod(x, -y)
+rem(x, y::Unsigned, ::RoundingMode{:Up}) =
+    throw(ArgumentError("rem(x, y, RoundUp) cannot be used with unsigned y")) # issue #34325
 rem(x, y, r::RoundingMode{:Nearest}) = x - y * div(x, y, r)
 rem(x::Integer, y::Integer, r::RoundingMode{:Nearest}) = divrem(x, y, r)[2]
 
diff --git a/test/numbers.jl b/test/numbers.jl
index faaa3d293626d..f1b40cf3653b0 100644
--- a/test/numbers.jl
+++ b/test/numbers.jl
@@ -1751,6 +1751,13 @@ end
             @test rem(typemin(T), T(-1)) === T(0)
             @test mod(typemin(T), T(-1)) === T(0)
         end
+        @testset "issue #34325" for S in (Int8, Int16, Int32, Int64, Int128)
+            U = unsigned(S)
+            @test rem(S(10), S(7), RoundUp) == -4
+            @test rem(U(10), S(7), RoundUp) == -4
+            @test_throws ArgumentError rem(S(10), U(7), RoundUp)
+            @test_throws ArgumentError rem(U(10), U(7), RoundUp)
+        end
     end
     @testset "issue #4156" begin
         @test fld(1.4, 0.35667494393873234) == 3.0