During the service lifetime of gravity dams, seepage flow could adversely affect the dam stability and its stress distribution. In investigating the reliability of gravity dams, it holds paramount importance to account for the seepage effects. In this study, an efficient reliability analysis is conducted to evaluate the stability and stress distribution of gravity dams incorporating the influence of seepage effects. This analysis involves integrating the response surface method and random finite element approach. For a hydropower station project, the key uncertain parameters affecting the stability and stress distribution of gravity dams are identified through a parametric sensitivity analysis. Using the response surface method, the performance function for the anti-sliding stability safety factor of gravity dams under the seepage effects is established, and the failure probability considering multiple failure modes is calculated. Meanwhile, the simulated results are compared with those obtained without considering the seepage effects. The influence of key uncertainty parameters on the failure probability of gravity dam is quantitatively analyzed by the probabilistic failure analysis. These findings show that accounting for seepage effects leads to higher failure probabilities, indicating that neglecting these effects may underestimate the likelihood of dam failure. In comparison with the three failure modes, the heel cracking of the gravity dam and sliding instability along dam-foundation interface are most likely to occur, followed by the dam toe cracking. The results could provide a theoretical foundation and technical guide for evaluating the reliability of practical dam projects.