A model based on axially moving material is developed to study transverse vibration in roller chain drives. A unique feature of the work presented in this study is that impact, polygonal action and external periodic load have been included through chain tension and boundary conditions and periodic length change is also considered. The impact between the engaging roller and sprocket surface is modeled as a single impact between two elastic bodies and the modeling of the polygonal action is based on a four bar mechanism (rigid four bar at low speeds, elastic four bar at moderate and high speeds). At low and medium operating speeds, the system equation of motion for the chain span is expressed as a mixed type partial differential equation with time-dependent coefficients and time-dependent boundary conditions. At high operating speeds, the system equations of motion are two partial differential equations for transverse and longitudinal vibrations respectively and they are nonlinearly coupled The effects on transverse vibration of center distance, the moment of inertia of the driven sprocket system, static tension, and external periodic load are presented and discussed. Solutions are obtained by a finite difference method and Galerkin’s method.