Time-dependent reliability models, failure rate models, and lifetime distribution models of belt drive systems are developed in this paper, which take geometric parameters, material parameters, and motion parameters as the input and consider the dynamic properties of the belt drive systems. Most of the reliability models of belt drive systems are static models. The proposed models can take into account the time-dependent statistical properties of dynamic stress process. Moreover, the stiffness degradation is considered in the established models, whose influences on reliability indices are analyzed in case study. The results show that stiffness degradation has significant impacts on reliability, failure rate, and lifetime distribution. In addition, sensitivity models of reliability with respect to input parameters are constructed, which can be used for the guidance of safe design of belt drive systems.