Industry is increasingly using additive manufacturing processes because of the speed and economy with which they can produce components of complex geometry. Among these processes, one of the most interesting is the Fused Filament Fabrication (FFF) technique, which allows the moulding of thermoplastic polymers reinforced with chopped or continuous fibres. The applicability of this technology on an industrial scale is linked to the ability to model and predict the mechanical properties of the produced parts. To date there is no universally accepted strategy to solve this issue. In this study, a multiscale modelling method based on numerical homogenization is proposed to properly simulate the mechanical performance of parts manufactured by using FFF. The mechanical behaviour of specimens was studied by means of a FEM software at different scales: microscopic, mesoscopic and macroscopic, showing the influence of the specific microstructure of each size level on the next scale. The effectiveness of the proposed models was evaluated by means of a wide experimental campaign, which tested specimens reinforced with short fibres and specimens reinforced with a combination of chopped and continuous fibres. The comparison of the mechanical properties estimated by using the numerical models with the experimental data showed a good correlation demonstrating the capabilities of the proposed approach.