One of the objectives of this thesis is to analyze the computational cost of the Monte Carlo method applied to a toy problem concerning the dynamics of a mechanical system with uncertainties in the friction force. The system is composed by an oscillator placed over a moving belt. The existence of dry friction between the two elements in contact is considered. Due to a discontinuity in the frictional force, the resulting dynamics can be divided into two alternating phases, called stick and slip. In this study, a parameter of the dynamic friction force is modeled as a random variable. Uncertainty propagation is analyzed by applying the Monte Carlo method, considering three different strategies to compute approximations to the initial value problems that model the system s dynamics: NV) numerical approximations computed with the Runge-Kutta method of 4th and 5th orders, with variable integration time-step; NF) numerical approximations computed with the Runge-Kutta method of 4th order, with a fixed integration time-step; AN) analytical approximation obtained with the multiple scale method. In the NV and NF strategies, for each parameter value, a numerical approximation was calculated, whereas for the AN strategy, only one analytical approximation was calculated and evaluated for the different values of parameters considered. The run-time and the storage are among the random variables of interest associated with the computational cost of the Monte Carlo method. Due to uncertainty propagation, the system response is a stochastic process given by a random sequence of stick and slip phases. This sequence can be characterized by the following random variables: the transition instants between the stick and slip phases, their durations and the number of phases. To study the random processes and the variables related to the computational costs, statistical models, normalized histograms and scatterplots were built. Afterwards, a joint analysis was performed to study the dependece between the variables of the random process and the computational cost. However, the construction of these analyses is not a simple task due to the impossibility of viewing the distributionto of joint distributions of random vectors of three or more.