The existence of weak shock wave solutions for discrete velocity models of the Boltzmann equation is proved. Specifically, consider triples (M−M+,c) of two Maxwellians M−M+and shock speeds c ∈ ℛ satisfying the Rankine-Hugoniot conditions. The triple (M−, M−, c) satisfies these conditions trivially for anyc. Ifc0is chosen to be such that the manifold defined by the Rankine-Hugoniot conditions exhibits a transcritical bifurcation at C0, then we prove that there is a one-sided, one-parameter family of triplesM−, M+()andc(), with M+(0) =M−and c(0) = c0, such that there is a rarefied shock wave solution for the discrete velocity model connectingM−with M+(), moving with shock speed c(), and satisfying the entropy condition.