Natural processes have been taken highly attention for many years and various methods have been used to find a proper solution to the processes. Striking physical systems are adequately modelled by the Duffing equation, which describes an oscillator with various nonlinearities. Since many difficulties are encountered in numerically solving the problems governed by the Duffing equation with damping effect, a new stochastic approach based on Monte Carlo technique has been proposed to handle it. To properly realize the simulated behavior of the processes, detailed discussion has been carried out in the present work.