This paper presents an efficient method to compute the failure probability of a geotechnical system, which is based upon numerical integration of the cumulative distribution function (CDF) of the performance function. This new method is inspired by the concept of the vertex method often used in conjunction with fuzzy sets theory; however, new approach is taken to account for the probabilistic feature of the uncertain input parameters. In the new method, only the deterministic analysis of the system performance and the evaluation of the joint probability of the uncertain input parameters are required. The proposed new method is a deterministic approach, easy to follow and apply; no Monte Carlo simulation is required. Through an example study of a shallow strip foundation, the effectiveness and the efficiency of the proposed new method, in terms of the accuracy and the computational effort, respectively, are demonstrated.