To enhance the launch capacity and performance, nearly all active launch vehicles incorporate two or more stages. During the launch process, gradual reduction of the launch vehicle mass is achieved by separating and discarding the spent propellant stages, which plays a vital role in ensuring the safety of the launch vehicle and successful launches. During the manufacturing and assembly processes of launch vehicle components, inherent deviations are inevitably encountered. These deviations may lead to a scenario where the launch vehicle is unable to execute separation maneuvers as per the intended plan, consequently directly impacting the stability of the separation body's attitude and potentially resulting in mission failure. The principles of stage separation of launch vehicles and dynamic governing equations are elucidated. Utilizing the Modelica language, models for the first stage and second stage of carrier rockets are developed to account for parameter deviations. Additionally, force models, explosive bolt models, separation gap models, and initial state models are established. These components are then assembled using a block-diagram and interconnection approach to construct a comprehensive Modelica model for the stage separation system of launch vehicles. The correctness of the model is verified through comparison of simulation results with an Adams model. Due to manufacturing and force deviations following certain probability distributions, such as uniform, normal, and Weibull distributions, a Monte Carlo shooting method is employed to conduct reliability simulation and analysis of the launch vehicle stage separation process that considers these deviations. The simulation results indicate that this approach can identify adverse conditions during stage separation, providing design engineers with the minimum separation gap under extreme scenarios, thus optimizing the design margin for the separation system.