The influence of wind loads on the driving behavior of ground vehicles is an important economical, safety, and comfort issue. The crosswind performance is of great interest, as violent lateral winds can cause major accidents or will at least make the driver and the passengers feel very uncomfortable and insecure. In this paper, a sampling based methodology for the analysis of stochastic ground vehicle systems is presented. Starting from the well known Monte Carlo method more sophisticated reliability methods with higher efficiency are introduced and their advantages and drawbacks are critically reviewed. Furthermore, probabilistic sensitivity analyses are presented, which can be used to quantify the importance of the random variables on the response of the vehicle system. The influence of the parameters of the probability density functions is investigated by means of a novel response surface method. The mentioned approach is applied to a nonlinear road vehicle model under strong crosswind excitation for which the failure probabilities and the sensitivities are computed.