We continue our investigation of stochastic lattice gases as a (highly parallel) means of simulating given PDEs, in this case Burgers' equation in one dimension. The lattice dynamics consists of stochastic unidirectional particle displacement, and our attention is turned toward the reliability of the model, i.e., its ability to reproduce the unique physical solution of Burgers' equation. Lattice gas results are discussed and compared against finite-difference calculations and exact solutions in examples which include shocks and rarefaction waves.