We describe how ab initio molecular dynamics can be used to determine the Hugoniot locus (states accessible by a shock wave) for materials with a number of stable phases, and with an approximate treatment of plasticity and yield, without having to simulate these phenomena directly. We consider the case of bulk silicon, with forces from density-functional theory, up to 70 GPa. The fact that shock waves can split into multiple waves due to phase transitions or yielding is taken into account here by specifying the strength of any preceding waves explicitly based on their yield strain. Points corresponding to uniaxial elastic compression along three crystal axes and a number of postshock phases are given, including a plastically yielded state, approximated by an isotropic stress configuration following an elastic wave of predetermined strength. The results compare well to existing experimental data for shocked silicon.