This work aims to develop a probabilistic analysis methodology for the behavior of a mass-spring-damper system subjected to random loads, modeled as stationary stochastic processes, addressing the problem both numerically and analytically. This approach is justified by the relevance of random vibrations in various engineering problems. With the aid of MATLAB, algorithms based on the Monte Carlo methodology were implemented, involving the generation of pseudorandom values of random variables, the construction of statistical models, and the analysis of the convergence between theoretical and sample statistics. The analysis tools employed include envelope plots, univariate and bivariate histograms, Wasserstein distances, spectral densities of the response, and investigations into the influence of the system s damping on the convergence of the response to a stationary stochastic process. Finally, the results of the analytical and numerical approaches were compared. The analytical solution was obtained through the derivation of the dynamic equation, while the numerical approximations were calculated using the Runge-Kutta method. The comparison evaluated advantages such as computational cost and the applicability of the methodology to more complex systems