A theory is developed for a selection rule governing collisions in a particle simulation of rarefied gas‐dynamic flows. The selection rule leads to an algorithmic form that is highly compatible with fine grain parallel decomposition, allowing for very efficient utilization of supercomputers having vector or massively parallel single instruction multiple data (SIMD) architectures. A comparison of shock‐wave profiles obtained using both the selection rule and Bird’s direct simulation Monte Carlo (DSMC) method show excellent agreement. This serves to establish the validity of the method, as the DSMC method is known to compare well with experimentally determined shock‐wave profiles. In addition, the equation on which the selection rule is based is shown to be directly related to the time‐counter procedure in the DSMC method, further establishing their equivalence. The results of several example simulations of representative rarefied flows are presented, for which the number of particles used ranged from 106to 107, demonstrating the greatly improved computational efficiency of the method.