This Bureau of Mines report describes a technique for determining the confining pressures that must be provided for stabilizing underground openings in incompetent rock. The technique is adapted for use with a nonlinear finite-element computer code, nonsap, to obtain stabilization pressures for linear or nonlinear stress distributions in the rock media around the excavation. This analysis permits a point-wise calculation of active rock pressures that depend on the values of shear stress and strength along the excavation surface. The approach is applied to the solution of several sample problems. The results show that both the magnitude and the distribution of stabilizing confining pressures are significantly influenced by rock and joint strengths, joint orientation, and biaxial nature of the load field.