[en] Introduction In the early phases of the intense underground explosions contemplated in peaceful applications the rock near the explosive exhibits fluid behaviour; at great distances its behaviour can usefully be investigated in terms of linear elasticity; and at intermediate distances we think of a solid exhibiting various inelastic effects including cracking and tensile fracture. The present paper outlines a mathematical model that attempts to include in some degree the main features of this range of behaviour. A more detailed treatment than is given here, and its relationship to the work of others, is given in a paper by the authors. A computer program ATHENE has been written based on this model and its use is illustrated by examining some aspects of two types of explosions. One is a chemical explosion which eventually formed a crater and the other a nuclear explosion which remained wholly contained