In this work, the first two-dimensional mesoscopic model has been implemented to study the mechanical behaviour of concrete reinforced with recycled tyre rubber as an aggregate. In particular, the replacement of different percentages of coarse aggregate by rubber has been analysed. Four phases have been discretised for the modelling: the aggregate, the rubber, the mortar, and its corresponding interfacial transition zones. For the model implementation, a Python script has been developed to generate a random distribution of circular aggregates from a size distribution curve. A plasticity model with available damage in the Abaqus/Explicit finite element code library has been used. In order to analyse the variation of mechanical properties with the incorporation of rubber in concrete, uniaxial compression tests have been simulated. The obtained results were compared with experimental data and an analytical model extracted from the literature. These investigation findings demonstrate the potential of the developed numerical tool for designing reinforced concrete structures that incorporate rubber as coarse aggregate.