The numerical modeling of damage and crack propagation in concrete and concrete structures has evolved considerably in the past years. In this contribution, a higher order continuum model is used to model the failure behavior of single-edge notched (SEN) and double-edge notched (DEN) concrete beams loaded in four-point-shear. Different types of boundary conditions, i.e. with freely rotating, fixed or constrained loading supports, are investigated and the experimentally observed curved crack paths are compared with the numerical simulations. The influence of the ratio of the compressive strength and the tensile strength is scrutinized and its relation with the failure mechanism is investigated. It is shown that an isotropic gradient-enhanced damage model permits to obtain a good agreement between experimental results and numerical simulations.