The design requirement of a mechanical system with motion mechanisms is to ensure the successful implementation of its motion functions. Aiming at the characteristics of motion mechanisms, a reliability allocation methodology is proposed. Since motion reliability plays an important role in motion mechanisms, a system decomposition is extended to map motion functions with subsystems. Combined with the analytic hierarchy process model, the subsystem contribution factor is developed. For motion mechanisms, the nondestructive fault events that have a significant impact on motion reliability are considered in the potential reliability improvement factor. To assist in evaluating the criticality of failures, the transformed failure severity factor is utilized. In addition, the dynamic performance factor is developed to evaluate the motion performance of the systems. Then, due to the interactions between the subsystems, the copula theory is applied to investigate the failure dependence, and the reliability model of the system to be apportioned is established. Furthermore, an engineering case about a mechanical system of an aircraft is presented to illustrate the applicability and rationality of the proposed method. The result shows that the reliability allocated to the subsystems is decreased when the failure dependence is considered, which is more reasonable in engineering practice.