The fundamental theories of simulating blast effects in elastic and elastoplastic media are presented in this monograph. Both classical and modern methods for modelling the processes of rock breakage by blasting are described. Contemporary methods for recording the processes occurring at high speeds are also presented. Physical and mathematical models of the major phenomena associated with blasting in open-cast and underground mines are illustrated. This monograph is intended for professionals involved in research and in the utilisation of blast energy in various sectors of the national economy.