Large deformation and rapid pressure propagation take place inside the rock mass under the dynamic loads caused by the explosives, on quarry faces in order to extract aggregate material. The complexity of the science of rock blasting is due to a number of factors that affect the phenomenon. However, blasting engineering computations could be facilitated by innovative software algorithms in order to determine the results of the violent explosion, since field experiments are particularly difficult to be conducted. The present research focuses on the design of a Finite Element Analysis (FEA) code, for investigating in detail the behavior of limestone under the blasting effect of Ammonium Nitrate & Fuel Oil (ANFO). Specifically, the manuscript presents the FEA models and the relevant transient analysis results, simulating the blasting process for three types of limestone, ranging from poor to very good quality. The Finite Element code was developed by applying the Jones-Wilkins-Lee (JWL) equation of state to describe the thermodynamic state of ANFO and the pressure dependent Drucker-Prager failure criterion to define the limestone plasticity behavior, under blasting induced, high rate stress. A progressive damage model was also used in order to define the stiffness degradation and destruction of the material. This paper performs a comparative analysis and quantifies the phenomena regarding pressure, stress distribution and energy balance, for three types of limestone. The ultimate goal of this research is to provide an answer for a number of scientific questions, considering various phenomena taking place during the explosion event, using advanced computational tools.