A study on the applicability of the Monte Carlo method in the analysis of the dynamical behavior of motorcycles subject to road excitation is presented. To this end, a time-domain numerical simulation of the response of a motorcycle modeled as a linear four-degree-of-freedom (4-DOF) system, and traveling at constant speed is carried out. To validate the accuracy of the solutions obtained, the linear 4-DOF model is also analyzed using the frequency domain approach. Although the Monte Carlo simulation can be computationally costly, it provides an excellent scheme of analyzing, as well, non-linear systems, in which case the frequency domain approach cannot be applied. In this context the applicability of auto-regressive (AR) and autoregressive-moving-average (ARMA) filters for efficient implementation of the Monte Carlo simulation is pointed out. Furthermore, a practical engineering approach is presented for improved road roughness power spectral density (PSD) representation, and statistical parameters of the excitation signals synthesized.