This research is devoted to the construction of a probabilistic model of uncertainties for a rigid multibody dynamical system dynamicmade up of uncertain rigid bodies. We first construct a stochastic model of an uncertain rigid body by replacing the mass, the center of mass and the tensor of inertia by random variables. The prior probability distributions of the stochastic model are constructed using the maximum entropy principle under the constraints defined by the available information. The generator of independent realizations corresponding to the prior probability distribution of these random quantities are developed. Then, several uncertain rigid bodies can be linked each others in order to calculate the random response of a multibody dynamical system. An application is proposed to illustrate the theoretical development.