Abstract: When using the Smoothed Finite Element Method (S-FEM) for numerical simulations, traditional tetrahedral and hexahedral grids have certain limitations in accuracy and adaptability. To address this issue, a new S-FEM analysis program based on polyhedral elements was developed. Its computational accuracy and mesh convergence were verified using a classical cantilever beam model. Subsequently, taking the Xichou concrete gravity dam as a case study, a high-quality finite element model with polyhedral elements was established. Based on two indicators(crest displacement and damage index), the vulnerability of the gravity dam was evaluated using the Incremental Dynamic Analysis (IDA) method. The results show that under both design and check seismic ground motions, the damage levels of the gravity dam are relatively low, with over 95% probability of only minor damage and a zero probability of dam failure. The proposed method innovatively combines S-FEM with polyhedral elements, improving the efficiency and accuracy of finite element analysis and providing a powerful tool for seismic design of dams. However, further improvements to the program are needed when dealing with complex problems.