This article aims to evaluate the sliding stability of a gravity dam with a foundation failure mechanism characterized by a pre-existing subhorizontal joint set acting as a sliding plane, and with a potential failure path that extends through the rock mass. The safety factor is estimated using a combination of joints and rock mass strengths, using the criteria of Barton and Choubey and Hoek and Brown, respectively. Nonassociative flow rule in the rock mass has been incorporated using a constant dilation angle. The finite difference program FLAC 6.0 is employed to validate the model. The proposed analytical model provides results that are very similar to those computed with FLAC; however, as the new formulation can be implemented in a spreadsheet, the computational cost of the proposed model is significantly smaller, hence allowing to more easily conduct parametric analyses of the influence of the different input parameters on the dam’s safety.