diff --git a/src/oneAPIKernels.jl b/src/oneAPIKernels.jl
index c35cc629f..2fb85a968 100644
--- a/src/oneAPIKernels.jl
+++ b/src/oneAPIKernels.jl
@@ -175,7 +175,11 @@ end
 end
 
 @device_override @inline function KA.__index_Global_Linear(ctx)
-    return get_global_id()
+    # The hardware global id only equals the linear index into `ndrange` when the work-group
+    # size evenly divides every dimension of it; otherwise KernelAbstractions pads the range,
+    # and the id has to be mapped through the iteration space (as the CPU back-end does).
+    I = @inbounds KA.expand(KA.__iterspace(ctx), get_group_id(), get_local_id())
+    return @inbounds LinearIndices(KA.__ndrange(ctx))[I]
 end
 
 @device_override @inline function KA.__index_Local_Cartesian(ctx)
diff --git a/test/kernelabstractions.jl b/test/kernelabstractions.jl
index 48bbe1cb7..3dd4ed66b 100644
--- a/test/kernelabstractions.jl
+++ b/test/kernelabstractions.jl
@@ -6,3 +6,61 @@ skip_tests=Set([
     "Convert", # Need to opt out of i128
 ])
 Testsuite.testsuite(oneAPIBackend, "oneAPI", oneAPI, oneArray, oneDeviceArray; skip_tests)
+
+using LinearAlgebra
+using KernelAbstractions: @kernel, @index
+
+@kernel function linear_index_kernel!(out)
+    i = @index(Global, Linear)
+    @inbounds out[i] = i
+end
+
+# When the work-group size does not divide a dimension of `ndrange`, KernelAbstractions pads
+# the range: the hardware global id then differs from the linear index into `ndrange`
+# (JuliaGPU/oneAPI.jl#509).
+@testset "padded ndrange (#509)" begin
+    @testset "@index(Global, Linear)" begin
+        backend = oneAPIBackend()
+        cases = [
+            # ndrange => explicit work-group sizes (`nothing` lets the back-end choose)
+            (513,) => (nothing, (32,), (256,)),
+            (513, 3) => (nothing, (32, 1), (256, 2)),
+            (3, 513) => (nothing, (1, 32), (2, 256)),
+            (64, 4, 500) => (nothing, (256, 4, 1), (32, 1, 2), (7, 3, 5)),
+            (64, 4, 500, 3) => (nothing, (64, 4, 1, 1), (16, 1, 7, 2)),
+        ]
+        for (ndrange, workgroupsizes) in cases, workgroupsize in workgroupsizes
+            out = oneAPI.zeros(Int, prod(ndrange))
+            linear_index_kernel!(backend)(out; ndrange, workgroupsize)
+            KernelAbstractions.synchronize(backend)
+            @test Array(out) == 1:prod(ndrange)
+        end
+    end
+
+    @testset "getindex" begin
+        x = randn(Float32, 513, 3)
+        dx = oneArray(x)
+        @test Array(dx[:, 1:2]) == x[:, 1:2]
+
+        x = rand(Float32, 64, 4, 500, 3)
+        dx = oneArray(x)
+        @test Array(dx[:, 2, :, :]) == x[:, 2, :, :]
+        @test Array(dx[2, :, :, :]) == x[2, :, :, :]
+        @test Array(dx[:, :, 2, :]) == x[:, :, 2, :]
+        @test Array(dx[:, :, :, 2]) == x[:, :, :, 2]
+    end
+
+    @testset "permutedims" begin
+        x = rand(Float32, 64, 4, 500, 3)
+        dx = oneArray(x)
+        @test Array(permutedims(dx, (3, 1, 4, 2))) == permutedims(x, (3, 1, 4, 2))
+        @test Array(permutedims(dx, (2, 1, 3, 4))) == permutedims(x, (2, 1, 3, 4))
+    end
+
+    @testset "rmul!" begin
+        x = rand(ComplexF32, 64, 1000, 16)
+        dx = oneArray(x)
+        rmul!(dx, 2.0f0)
+        @test Array(dx) == x .* 2.0f0
+    end
+end