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Analyzing the seepage and stability analysis of embankment dams built on deep overburden layers is an essential aspect of dam design and operation and is of significance to ensure the safe and effective operation of geotechnical and hydraulic structures in reservoir sites. However, in most existing studies, the seepage and dam slope stability were analyzed separately without considering the interaction between the two fields; thus, the actual operating state of the dam could not be accurately reflected. In this paper, an embankment dam located in Yulin, Shaanxi Province, China, built on a deep overburden layer, was selected as a case study for illustration. Considering the hydrogeological and engineering design information of this project, a three-dimensional fine finite element model reflecting the main characteristics of the reservoir site was established. COMSOL Multiphysics software, which is particularly suitable for multifield coupling calculations, was used to conduct a multifield coupling analysis of the safety state of embankment dams on deep overburden layers by modifying and customizing the porous media and subsurface flow module and solid mechanics module. The method to solve the multifield coupling problem was clarified. Notably, the proposed coupling model involved many parameters, which might introduce uncertainties into the model, thereby requiring considerable work for calibration. Therefore, the Morris method was used to identify the sensitivity of the coupled model parameters to the output results. The results show that the established multifield coupling model can effectively address the seepage and stability problems of embankment dams on deep overburden layers, and the dam can safely operate under the existing design scheme. Even under the condition of a magnitude VIII earthquake at the check flood level, the dam does not experience seepage and slope failure. The safety factor of sliding failure of the dam slope is mainly influenced by the internal friction of saturated soil (φs), material cohesion (c), internal friction of unsaturated soil (φu), soil density (ρs) and Poisson's ratio (ν), while the influence of the seepage parameters is generally small. The methodology and results derived from this study can provide technical support and reference to evaluate the safety in terms of the seepage and anti-sliding stability of similar projects. [ABSTRACT FROM AUTHOR]