Fibre reinforced polymers (FRPs) exhibit high specific stiffness and damping capacity making them an excellent choice for aerospace applications. However, absence of accurate predictive tools (analytical/numerical) are limiting their optimal use in industry. High fidelity numerical methods offer potential solution that would lead to an accurate prediction of their mechanical properties, resulting in relatively faster material concept development with significantly reduced testing costs and time. In this work, numerical simulations are performed to predict the anisotropic linear-viscoelastic response of the unidirectional (UD) FRPs at both fibre-matrix level (microscale) and laminate level (mesoscale). At micro-scale, a new algorithm is developed to generate virtual representative microstructures and their spatial characteristics are compared to those observed in real fibre composites micrographs. A virtual material test bed has been developed, which enables performing automatic Monte-Carlo (MC) analysis of stochastic volume elements using periodic boundary conditions. Based on such an analysis, a new minimum RVE size has been proposed to predict the homogenized anisotropic viscoelastic response of the UD FRPs. Predictions of the numerical model have been validated using experiments performed on UD CFRP beams with an accuracy of 15% for the case of stiffness properties. It has been shown that none of the current theories accurately predict the full anisotropic response and a new simple interpolative analytical model has been proposed, allowing the designers to predict stiffness and damping properties of FRPs without performing computationally intensive MC simulations. The virtual material test bed has also been extended to study the effects of novel, non-cylindrical fibre shapes as well as the effects of geometric and mechanical properties of fibre interphase on the mechanical performance of UD FRPs. It has been found that unsymmetrical fibre shapes have minor increase in damping capacity due to marked stress concentrations. At macroscale, a constrained genetic algorithm has been developed and applied to the case of damping optimization in a hybrid FRP laminate with viscoelastic inserts, considering laminate layup, ply thickness and location of the viscoelastic inserts as the design variables.