Abstract: In this study, Cellular Neural Network (CNN�s) is applied to compute the transient response of mechanical vibrating systems along with popular numerical integration algorithms. The result of RK-Butcher algorithm is compared with Euler, RK-Gill algorithms and with analytic solutions of the mechanical vibrating system. Stability analysis for the RK-Butcher algorithm has been discussed. Error graphs for the mechanical vibrating systems are presented in a graphical form to show the efficiency of this RK-Butcher algorithm.