Some of the most used strengthening techniques for reinforced concrete structures include the increase of existing cross-sections. The monolithic behaviour of the strengthened elements depends basically on the interface between the substrate and the new concrete layer. A complete numerical model capable of dealing with the composite response of these RC elements is still missing. Such a model mainly depends on the interface behaviour, namely shear friction and dowel action. A numerical model is calibrated using experimental data carried out to assess the longitudinal shear strength between two concrete layers with different values of added rein- forcement. A parametric study is developed to identify the influence of the following parameters on the interface behaviour: elastic stiffness; cohesion; internal friction angle; fracture energy; dilatancy; steel constitutive law and the bond-slip relation between connectors and concrete. The role of each parameter is clarified and the most relevant conclusions are presented.