For being able to design tensile reinforcement laps with confidence, a good understanding of the mechanical performance and failure process is required. In this study, the response of laps subjected to tension in plain and steel fibre reinforced concrete was investigated by nonlinear finite element analyses. For analysing reinforced concrete, the individual phases of the composite, namely concrete, steel and bond between steel and concrete, were modelled. For concrete, a damage-plasticity constitutive model was used. The stress-crack opening curve of concrete was calibrated to describe the influence of steel fibres on the cracking response. The results show that a small volume fraction of fibres improves the mechanical performance of tensile reinforcement laps significantly.