Abstract For rock slope engineering, uncertainty and variability are inherent in data collected on orientation and strength of discontinuities, yielding a range of results. Unfortunately, conventional deterministic analysis based on the factor of safety concept, requires a fixed representative value for each parameter without regard to the degree of uncertainty involved. Therefore, the deterministic analysis fails to properly represent uncertainty and variability, so common in engineering geology studies. To overcome this shortcoming, the probabilistic analysis method was proposed and used for more than a decade in rock slope stability analysis. However, most probabilistic analyses included a deterministic model as part of the analysis procedure causing subsequent problems, which went uncorrected. The objectives of this paper are to develop a solution for these difficulties in probabilistic analyses and to propose an appropriate simulation procedure for the probabilistic analysis of rock wedge failures. As part of the solution, probability of kinematic instability and probability of kinetic instability are evaluated separately to provide a proper, combined evaluation for failure probability. To evaluate the feasibility of this new probabilistic approach, the procedure is applied to a practical example, a major, highway rock cut in North Carolina, USA. Results of the probabilistic approach are compared to those of the deterministic analysis; findings are significantly different, indicating that the deterministic analysis does not depict rock slope variations, particularly where significant scatter in parameter data occurs.