The study of concrete dam subjected to extreme loading conditions require theadoption of accurate constitutive equations. In this paper some recent results on the meso-scalesimulation of blast and penetration e ects on concrete will be discussed. The adopted meso-scale constitutive equation is the so-called Lattice Discrete Particle Model (LDPM) recentlyformulated at Rensselaer Polytechnic Institute. LDPM can accurately describe the macroscopicbehavior of quasi-brittle materials, and especially concrete, during elastic, fracturing, softening,and hardening regimes. Tensile dominated experimental tests under both dynamic conditionswere numerically simulated. After presenting examples of simulations relevant to quasi-staticand dynamic concrete behavior, LDPM simulation of the e ect of air blast pressure, on concretewill be discussed. Finally, the problem of the extrapolations of laboratory tests to actual in-situconditions is also presented.