Finite Element (FE) simulations are conducted to predict the viscoelastic properties of uni-directional (UD) fibre composites. The response of both periodic unit cells and random stochastic volume elements (SVEs) is analysed; the fibres are assumed to behave as linear elastic isotropic solids while the matrix is taken as a linear viscoelastic solid. Monte Carlo analyses are conducted to determine the probability distributions of all viscoelastic properties. Simulations are conducted on SVEs of increasing size in order to determine the suitable size of a representative volume element (RVE). The predictions of the FE simulations are compared to those of existing theories and it is found that the Mori-Tanaka (1973) and Lielens (1999) models are the most effective in predicting the anisotropic viscoelastic response of the RVE.