The distribution of molecular velocities in a strong shock wave is usually assumed to be bimodal, on the basis of mean free path arguments. Indeed, this assumption has been confirmed by Sakurai for the case of rigid sphere molecules. It turns out that such a confirmation is no longer possible when the intermolecular forces have sufficiently long ranges; in particular, it is shown that, for the case of a fully ionized gas, the Boltzmann equation is not satisfied by a bimodal distribution, regardless of the choice for the shock thickness parameter and Mach number. This breakdown of the bimodal solutions is ascribed to an inadequacy in the usual mean free path concept for a plasma, due to the dominance of weak collisions at high temperatures.