The polygon effect is a major factor affecting the dynamic characteristics of chain drive in oil saw chain system. It causes impact, noise and dithering of the saw chain and significantly affects the lifespan of oil saw. A simple analytical method is proposed for analyzing the dynamic response resulting from the polygon effect of an oil saw chain system by using the difference method for numerical approximation. A MATLAB program is implemented and then applied for the polygon effect analysis of a specific saw chain drive. Numerical results such as velocities and dynamic loads due to polygon effect are compared with experimental data to demonstrate the effectiveness of the new method. A good agreement is obtained. The proposed polygon effect analysis method can provide guidelines for oil saw chain design for better dynamic performance.