An account is given of a mathematical model for computing the axially symmetric, unsteady, compressible motion of rock driven by an explosive deriving its energy from chemical or nuclear processes. The rock very near the explosive may be vaporized by shock heating, at somewhat greater distances it may be melted, and over a considerable range of distances it will remain solid, exhibiting a variety of responses largely dominated by elastic-plastic behaviour beyond the scope of infinitesimal strain theory. Numerical tests of a Lagrangian computer program are described, and an illustrative example discusses some aspects of an actual explosion of 500 tons of TNT for which observations have been reported.