The vibrations have turn out to be all the time more significant in recent years owing to the present trend toward higher-speed machines and lighter structures. Most mechanical and structural systems have distributed mass, elasticity, and damping. Ordinary differential equations (ODEs) play a vital role in such mechanical and structural systems. In this paper we construct a Mathematical model and Simulink Model for the damped mass-spring system by using second law of motion to the masses with the forces acting by the spring and force by any external sources. Simulink Model developed by using block diagram from the different libraries of Simulink.