The direct simulation Monte Carlo method of modeling fluids requires sampling one or more random variables every time step for each particle. In this paper a "quiet Monte Carlo" technique is proposed that eliminates the random sampling and the noise it produces by deterministically generating a small number of computational particles. The technique is applied to particle equations of motion appropriate for modeling an Eulerian fluid. Results indicate that strong one- and two-dimensional shocks with large dynamic ranges are accurately represented with only a few particles per cell.