This paper deals with the analysis of the propagation of uncertainties in computational linear dynamics for linear viscoelastic composite structures in the presence of uncertainties. In the frequency domain, the generalised damping matrix and the generalised stiffness matrix of the stochastic computational reduced-order model are random frequency-dependent matrices. Due to the causality of the dynamical system, these two frequency-dependent random matrices are statistically dependent and their probabilistic model involves a Hilbert transform. In this paper, a computational analysis of the propagation of uncertainties is presented for a composite viscoelastic structure in the frequency range.