Recycled carbon fibre–reinforced epoxy (rCF/EP) composites and recycled glass fibre–reinforced epoxy (rGF/EP) composites were numerically investigated to examine their mechanical properties, such as uniaxial tensile and impact resistance, using finite element (FE) methods. The recycled composites possess unidirectional, long and continuous fibre arrangements. A commercially available Abaqus/CAE software was used to perform an explicit non-linear analysis with a macroscale modelling approach, assuming the recycled composites as both homogenous and isotropic hardening. Five composite types were subjected to a numerical study based on the recycled fibre’s volume fraction (40 and 60%) of rCF/EP and rGF/EP, along with (100%) fibreless cured epoxy samples. The materials were defined as elastoplastic with a continuum ductile damage (DUCTCRT) model. The experimental tensile test results were processed and calibrated as primary input data for the developed FE models. The numerical tensile results, maximum principal stress and logarithmic strain were validated with their respective experimental results. The stress–strain curves of both results possess a high accuracy, supporting the developed FE model. The numerical impact tests examined the von Mises stress distribution and found an exponential decrease in the stiffness of the composite types as their strength decreased, with the 60% rCF/EP sample being the stiffest. The model was sensitive to the mesh size, hammer velocity and simulation time step. Additionally, the total internal energy and plastic dissipation energy were measured, but were higher than the experimentally measured energies, as the FE models eliminated the defects from the recycled process, such as a poor fibre wettability to resin, fibre bundle formation in rCFs and char formation in rGFs. Overall, the developed FE models predicted the results for a defect-free rCF/EP and rGF/EP composite. Hence, the adopted modelling techniques can validate the experimental results of recycled composites with complex mechanical properties and damage behaviours in tensile and impact loading conditions.