Due to its simplicity and good statistical results, the Monte Carlo (MC) method is the most commonly technique used for uncertainty quantification. However, its computational cost is significant, and, in many cases, prohibitive. Fortunately, the MC algorithm can be can be parallelized, which may allows its use in complex simulations. In this sprit, this work presents a methodology for the parallelization of MC method in a cloud computing setting. The methodology is illustrated on a stochastic problem of structural dynamics, and the simulation results show good accuracy for low-order statistics. Also, this methodology shows a good performance in terms of processing-time and storage space usage.