Responses of multi degree of freedom systems under random excitations can be estimated by using Monte Carlo simulation. The equations of motion of an elastic pendulum system include nonlinear terms and show irregular characteristics under random excitation. While the magnitude of random excitation is small the response of an elastic pendulum shows borderlines. As the magnitudes of excitation increase, the responses show divergence with very large amplitudes of motion and the tendency is diverse dependent on the magnitude and type of random excitations and the ratio of natural frequencies.