Abstract The paper considers the failure study of concrete structures loaded by the pressure wave due to detonation of an explosive material. In the paper two numerical methods are used and their efficiency and accuracy are compared. There are the Smoothed Particle Hydrodynamics (SPH) and the Finite Element Method (FEM). The numerical examples take into account the dynamic behaviour of concrete slab or a structure composed of two concrete slabs subjected to the blast impact coming from one side. The influence of reinforcement in the slab (1, 2 or 3 layers) is also presented and compared with a pure concrete one. The influence of mesh density for FEM and the influence of important parameters in SPH like a smoothing length or a particle distance on the quality of the results are discussed in the paper