Given that s1 and s2 are two matrix with the same dimensions, you can do it in many ways, just the two first I can think of:
Join[s1, s2]
ArrayFlatten[{{s1}, {s2}}]
If you want to join s2 at the right of s2 instead of below:
Join[s1, s2, 2]
ArrayFlatten[{{s1, s2}}]
