In this study, the cylindricity error was integrated into the tolerance analysis of precision rotary assemblies using Jacobian–Torsor model. The contact method was developed to rapidly determine the actual fitting clearance through the virtual assembling of the mating cylindrical parts using Monte Carlo simulation. By modifying the expressions of small displacement torsors of the cylinder pairs, the actual fitting clearance between the bore and the shaft was taken into account, which overcame the shortage of Jacobian–Torsor model that the form error cannot be processed. The effects of the cylindricity error and the number of lobes on the actual fitting clearance and the functional requirements were analyzed in detail. The results show that the cylindricity error has significant influence on the actual fitting clearance and the final functional requirements, and it should not be ignored in the tolerance analysis for precision rotary assemblies.