In this study, a three-dimensional model of ball/plane contact was created using the Abaqus commercial software, which was then converted into a two-dimensional model for finite element simulations. The simulations were conducted to simulate tangential motion under various friction coefficients and load conditions, thereby assessing the wear behavior of Si3N4 ceramics. The accuracy of the simulation results was validated using the Hertz contact theory, indicating that the established finite element model can accurately predict the stress distribution and wear process of Si3N4 ceramics. Additionally, this study also explored the contact stress and wear behavior of Si3N4 ceramics coated with MoS2-TiN films and diamond/MoS2-TiN films. By comparing the simulation results under different conditions, this study provides valuable theoretical insights for improving the service life of mechanical components.