A sliding crack model is employed to simulate rock strength under dynamic compression. It is assumed that the growth and nucleation of a sliding crack array presented results in the shear fault failure and dominate the mechanical properties of rock material. The pseudo-tractions method is used to calculate the stress intensity factor of the sliding crack array under compression. With the utilization of a dynamic crack growth criterion, the growth of the sliding crack array is studied and the simulated strengths of a granite under dynamic compression are correspondingly obtained. It is concluded that the simulated rock strengths increase with increasing strain rates at different confining pressures, and the rising rates have a trend to decrease with increasing confining pressures. It is also indicated that the simulated rock strengths increase with increment of confining pressure at different strain rates, and the rising rates are almost identical at different strain rates. The simulation results are validated by the experimental data for the granite. Copyright (C) 2001 John Wiley & Sons, Ltd.