A plasticity based constitutive model with two yield surfaces is developed to model the nonlinear axial and volumetric behavior observed for rocks in triaxial compression. The failure surface is allowed to soften at low pressures to simulate fracturing. A method for treating the corner where the yield surfaces intersect is developed. In comparisons with experimental data, the model accurately predicts the axial response in triaxial tests. The model predicts too much dilation for low confining pressure triaxial tests. The constitutive model was used in conjunction with a finite element code to simulate axisymmetric indentation of rock. Because of the existence of the corner in the yield surface, the simulation was computationally too slow to be practical.