Abstract Suspension system is very important for comfort driving and travelling of the passengers. Therefore, this study provides a numerical tool for modeling and analyzing of a single degree of freedom nonlinear quarter locomotive model suspension system. Modal analysis places a vital role in designing the suspension system. In this paper presented the modal analysis of quarter locomotive model suspension system by considering the nonlinear spring stiffness. The modal and vertical equations of motions describing the suspension system were then solved theoretically for damping cases. The program was used successfully to solve the actual coupled equations and to plot the results.