As the performance of the box-type multiple launch rocket system(BMLRS) improves, its mechanical structures, particularly the plane clearance design between the slider on the rocket and the guide inside the launch canister, have grown increasingly complex. However, deficiencies still exist in the current launch modeling theory for BMLRS. In this study, a multi-rigid-flexible-body launch dynamics model coupling the launch platform and rocket was established using the multibody system transfer matrix method and the Newton-Euler formulation. Furthermore, considering the bending of the launch canister,a detection algorithm for slider-guide plane clearance contact was proposed. To quantify the contact force and friction effect between the slider and guide, the contact force model and modified Coulomb model were introduced. Both the modal and launch tests were conducted. Additionally, the modal convergence was verified. By comparing the modal experiments and simulation results, the maximum relative error of the eigenfrequency is 3.29%. thereby verifying the accuracy of the developed BMLRS dynamics model. Furthermore, the launch test validated the proposed plane clearance contact model.Moreover, the study investigated the influence of various model parameters on the dynamic characteristics of BMLRS, including launch canister bending stiffness, slider and guide material, slider-guide clearance, slider length and layout. This analysis of influencing factors provides a foundation for future optimization in BMLRS design.