The physical model and mathematical methods used in computing the behavior of detonation waves in real materials are described and used to study the detonation behavior of TNT. Data needed as input to the problem are the equation-of-state parameters of the reacted and unreacted phases and the reactionrate parameters. The equation-of-state data are derived from experimentally obtained Hugoniots of the explosive and from experimentally determined steady-state detonation velocities. Values for the rate parameters are obtained by matching the growth trajectories of computed waves with experimentally determined curves over a range of initiation pressures. Good agreement is found between calculated and observed reaction-zone thicknesses, and a trajectory computed for an initiation pressure significantly removed from those at which the rate parameters were evaluated showed fair agreement with experiment.