diff --git a/src/cgutils.cpp b/src/cgutils.cpp
index 06c06215dfad19..f3a7e5ea7e6d7a 100644
--- a/src/cgutils.cpp
+++ b/src/cgutils.cpp
@@ -524,7 +524,10 @@ static Type *julia_struct_to_llvm(jl_value_t *jt, jl_unionall_t *ua, bool *isbox
 #endif
                 unsigned llvm_alignment = DL.getABITypeAlignment((Type*)jst->struct_decl);
                 unsigned julia_alignment = jst->layout->alignment;
-                assert(llvm_alignment == julia_alignment);
+                // Check that the alignment adheres to the heap alignment.
+                assert(julia_alignment <= JL_SMALL_BYTE_ALIGNMENT);
+                if (llvm_alignment  <= JL_SMALL_BYTE_ALIGNMENT)
+                    assert(julia_alignment == llvm_alignment);
             }
 #endif
         }
diff --git a/src/datatype.c b/src/datatype.c
index 0bf85c8af246a2..ce7c46c24e7900 100644
--- a/src/datatype.c
+++ b/src/datatype.c
@@ -310,7 +310,10 @@ void jl_compute_field_offsets(jl_datatype_t *st)
         // Some tuples become LLVM vectors with stronger alignment than what was calculated above.
         unsigned al = jl_special_vector_alignment(nfields, lastty);
         assert(al % alignm == 0);
-        if (al)
+        // JL_SMALL_BYTE_ALIGNMENT is the smallest alignment we can guarantee on the heap.
+        if (al > JL_SMALL_BYTE_ALIGNMENT)
+            alignm = JL_SMALL_BYTE_ALIGNMENT;
+        else if (al)
             alignm = al;
     }
     st->size = LLT_ALIGN(sz, alignm);
diff --git a/test/vecelement.jl b/test/vecelement.jl
index 95209b143c28b5..49c34825def5ee 100644
--- a/test/vecelement.jl
+++ b/test/vecelement.jl
@@ -23,6 +23,13 @@ for i=1:20
     end
 end
 
+# Try various large tuple lengths and element types #20961
+for i in (34, 36, 48, 64, 72, 80, 96)
+    for t in [Bool, Int8, Int16, Int32, Int64, Float32, Float64]
+        call_iota(i,t)
+    end
+end
+
 # Another crash report for #15244 motivated this test.
 struct Bunch{N,T}
     elts::NTuple{N,Base.VecElement{T}}
@@ -65,3 +72,56 @@ a[1] = Gr(5.0, Bunch((VecElement(6.0), VecElement(7.0))), 8.0)
 @test a[2] == Gr(1.0, Bunch((VecElement(2.0), VecElement(3.0))), 4.0)
 
 @test isa(VecElement((1,2)), VecElement{Tuple{Int,Int}})
+
+# The following test mimic SIMD.jl
+const _llvmtypes = Dict{DataType, String}(
+    Float64 => "double",
+    Float32 => "float",
+    Int32 => "i32",
+    Int64 => "i64"
+)
+
+@generated function vecadd(x::Vec{N, T}, y::Vec{N, T}) where {N, T}
+    llvmT = _llvmtypes[T]
+    func = T <: AbstractFloat ? "fadd" : "add"
+    exp = """
+    %3 = $(func) <$(N) x $(llvmT)> %0, %1
+    ret <$(N) x $(llvmT)> %3
+    """
+    return quote
+            Base.@_inline_meta
+            Base.llvmcall($exp,
+               NTuple{N, VecElement{T}},
+               Tuple{NTuple{N,VecElement{T}},NTuple{N,VecElement{T}}},
+               x, y)
+    end
+end
+
+function f20961(x::Vector{Vec{N, T}}, y::Vector{Vec{N, T}}) where{N, T}
+    @inbounds begin
+        a = x[1]
+        b = y[1]
+        return vecadd(a, b)
+    end
+end
+
+# Test various SIMD Vectors with known good sizes
+for T in (Float64, Float32, Int64, Int32)
+    for N in 1:36
+        # For some vectortypes Julia emits llvm arrays instead of vectors
+        if N %  7 == 0 || N % 11 == 0 || N % 13 == 0 || N % 15 == 0 ||
+           N % 19 == 0 || N % 23 == 0 || N % 25 == 0 || N % 27 == 0 ||
+           N % 29 == 0 || N % 31 == 0
+            continue
+        end
+        a = ntuple(i->VecElement(T(i)), N)
+        result = ntuple(i-> VecElement(T(i+i)), N)
+        b = vecadd(a, a)
+        @test b == result
+        b = f20961([a], [a])
+        @test b == result
+        if N == 36
+            code_llvm(STDOUT, f20961, (Vector{Vec{N, T}}, Vector{Vec{N, T}}))
+        end
+    end
+end