Internal radial clearance (IRC) in roller bearings must be kept to a minimum to avoid non-synchronous vibration (NSV). However, tight IRC increases the risk of bearing durability so that initial clearance is often on the high side and then reduced if necessary when problems with NSV are detected. In rolling element bearings, non-synchronous vibration may be originated by nonlinear contacts, which strongly depend on the IRC. In this paper, instead of the commonly used Hertz contact theory, the Lagrangian multipliers method is adopted to handle the nonlinear contacts between rollers and the outer ring. In order to reduce computational costs, a modal reduction technique is used. The influence of the roller bearing parameters on the NSV is analyzed. Among the existing parameters, the IRC plays the most important role in controlling the NSV.