Numerical modeling methods for nonlinear hybrid systems have significant mathematical and practical importance. This article examines the analysis of systems that include both continuous and discrete components, as well as issues related to their numerical integration. The application of numerical methods based on an accurate model, their computational efficiency, and the correspondence of results to real systems are evaluated. Additionally, the composition of hybrid systems and the stability of their solutions are analyzed. The research results contribute to the expansion of theoretical and applied aspects of hybrid system modeling.