This work is devoted to the dynamic analysis of multiple collisions problems in discrete element system and multi-body system using the bi-potential method. The prediction-correction step for solving the collision impulse is generated by the bi-potential function and the Uzawa algorithm. An extension from discrete element system to multi-body system is completed and an improvement on existing research is realized. Three numerical examples are carried out to illustrate the accuracy and efficiency of the proposed method. Results show that the improved solution is closer to the analytic solution. In the discrete element system, the numerical solutions from the proposed method are in good agreement with those from linear complementarity problem (LCP) method. However, the numerical solutions of the proposed method are more stable in the multi-body system. Further, the in-house software FER/Mech is used to realize dynamic simulation of the entity object. By comparing the dynamic simulation with the experimental video, it can be verified that their motions are synchronous. In addition, the equation for solving the bi-potential coefficient of rigid bodies contains an unknown stability factor. This work gives the value range of the bi-potential coefficient, which provides a direction for future investigating of stability factor and speeds up the computing progress.