Because of increasing demands for using of rotating systems in high accuracy and high speed applications, in addition of specific condition of rotating systems, it is necessary to analyze these rotating systems characteristics. Tolerance analysis is a useful tool for estimating effects of dimensional and geometrical errors of effective parameters on functional characteristics in a mechanical system. Unlike other mechanical systems, in addition to the dimensional and geometrical errors, the accuracy of the rotary systems performance directly depend on the flexibility of parts and Non Repetitive Run-Out (NRRO) errors. In this paper, a new method is proposed for static and dynamic tolerance analysis of the rotary systems with the dimensional and geometrical errors, the flexibility effects, and the NRRO errors based on the tolerance zone model. First, using the small degrees of freedom concept, the dimensional and geometrical errors and the NRRO error are modeled in the tolerance zone. Then, based on a new strategy, the performance -assembly functions of the system for modeling the error propagation of the rotary system in the static and dynamic conditions are extracted. Then, using the proposed equations, sensitivities of the requirements such as the end of shaft position and the main natural frequency to tolerances are computed. To illustrate applicability of the proposed method, a rotary system is considered as a case study. Monte Carlo simulations are used for validation of the computational results from proposed method.