Rock blasting are usually carried out by drilling slender holes into a rock mass and detonating explosive charges in their interiors. The detonation produces a fast increase in the temperature surrounding the holes and a huge gas expansion that will apply high pressures on the walls. Crushing and fracturing of the rock will occur as a consequence of the shock waves generated by this dynamic loading. Blasting engineer should know the strength and deformation characteristics of rocks under dynamic loading in order to better understand and estimate the effects caused by the explosion. Rock blasting is a very complicate problem whose simulation, to avoid insurmountable mathematical difficulties, needs to be developed under some simplifying assumptions such as isotropy, linear elasticity and brittle behavior of the material. In this work a computational program based on the finite element method was developed for dynamic analyses of rock blasting. The fracturing is considered to be primarily caused by the stresses induced by P and SV waves. The effects of the gas pressure inside the fractures were neglected at the time being. The software has the following main features: automatic generation of finite element meshes while fracturing is still detected in the rock mass, numerical integration of the equations of motion in the time domain, use of fracture propagation criteria based on stress intensity factors in mixed mode I-II, consideration of silent mesh boundaries to absorb the incident stress waves and a penalty method to enforce the impenetrability condition between the surfaces of a same fracture, etc. The numerical examples herein presented qualitatively indicate that the proposed model is satisfactory for the case of dynamic fracturing of brittle rocks. They also discuss several important aspects related to the numerical simulation, such as the number and distribution of predominant fractures around the blasting hole, the finite element size, loss of symmetry due to mesh configurations, etc.