A new model is presented for simulating rotational energy relaxation in the direct simulation Monte Carlo method (DSMC) using discrete distributions. The method extends the phenomenological approach generally employed that simulates the distribution as a continuum. The discrete approach simulates the mechanics of relaxation for the rigid rotor model. The theory is developed and combined for use with an existing model for simulating the rate of rotational relaxation. A number of test problems are then considered. Each set of flow conditions is chosen because of the availability of experimental data. Some of the experimental measurements provide rotational energy distributions thus allowing detailed comparison with the numerical simulations. Generally, the comparisons are quite favorable, although it is indicated that more sophisticated models are required to simulate some of the detailed structure of the energy distributions observed experimentally.