Computer-aided analysis of rigid-body mechanisms is combined with the finite element analysis of flexible structures to develop a computer model and derive the equation of motion, incorporating the Lagrange multiplier, to be used in the dynamic analysis of multi-rigid-body mechanisms mounted on flexible support structures. The resulting equations are solved by numerical integration. Predicting and analyzing the performance of the full system, including the motion of the system components and the forcing condition, during the engineering design process will promote the success of the entire system. Finally, a machine gun system with a flexible mount is given as a numerical example. The results reveal that the interaction between the rigid-body mechanisms and its flexible support structures importantly determines the performance of whole system. This study considers only the planar case. Our future work will propose a more complicated fully three-dimensional model.