The performance of advanced isotropic constitutive laws under complex stress states in plain and reinforced concrete specimens is investigated. Three different formulations are chosen: original Mazars model, Mazars μ model and model proposed by Pereira and coworkers. The degradation of the material in all formulations is described via a single variable, but a strain/stress state is taken into account via quite sophisticated relationships. In order to better reproduce experimentally observed stress-strain curves in uniaxial tension and compression, some modifications and extensions are proposed. An integral non-local approach is used to ensure FE mesh insensitive results. Two benchmarks are simulated. Nooru-Mohamed test is chosen to analyse numerically the growth of cracks in plain concrete under mixed-mode stress conditions. A geometrically scaled set of longitudinally reinforced beams under four-point bending load serves to assess the ability of reproducing different failure mechanisms. All results obtained from calculations are compared with experimental outcomes.