A new nonparametric probabilistic approach is presented for modeling random uncertainties in transient linear elastrodynamics. The information used does not require a description of the local parameters of the mechanical model. The probability model is constructed in the generalized coordinates associated with the elastic eigenmodes. The available information is constituted of the algebraic properties of the generalized mass. damping and stiffness matrices which have to be positive-definite symmetric matrices. and the knowledge of these matrices for the mean reduced matrix model. The convergence of the stochastic solution with respect to the dimension of the random reduced matrix model is analysed.