A finite element model for fully automatic simulation of multi-crack propagation in concrete beams is presented. Nonlinear interface elements are used to model discrete cracks with concrete tensile behaviour represented by the cohesive crack model. An energy-based crack propagation criterion is used in combination with a simple remeshing procedure to accommodate crack propagation. Various local arc-length methods are employed to solve the material-nonlinear system equations characterised by strong snap-back. Three concrete beams, including a single-notched three-point bending beam (mode-I fracture), a single-notched four-point shear beam (mixed-mode fracture) and a double-notched four-point shear beam (mixed-mode fracture), are modelled. Comparisons of the numerical results with experimental data show that this model is capable of fully automatically modelling concrete tensile fracture process with accurate pre/post-peak load–displacement responses and crack trajectories. Its mesh-objective nature, together with the high efficiency of the energy crack propagation criterion, makes using coarse meshes to obtain reasonably accurate simulations possible. The local arc-length numerical algorithms are found to be capable of tracking complex equilibrium paths including strong snap-back with high robustness, generality and efficiency.