  Solvable vertex models in a ferromagnetic regime give rise to soliton
cellular automata at q=0. By means of the crystal base theory, we study a class
of such automata associated with the quantum affine algebra U_q(g_n) for non
exceptional series g_n = A^{(2)}_{2n-1}, A^{(2)}_{2n}, B^{(1)}_n, C^{(1)}_n,
D^{(1)}_n and D^{(2)}_{n+1}. They possess a commuting family of time evolutions
and solitons labeled by crystals of the smaller algebra U_q(g_{n-1}).
Two-soliton scattering rule is identified with the combinatorial R of
U_q(g_{n-1})-crystals, and the multi-soliton scattering is shown to factorize
into the two-body ones.
