Physical and hydrodynamic processes accompanying explosions of condensed explosives and fuel-air mixtures have been considered. Wide-range equations of the state of explosion products and air have been derived. A physical model and a program code based on the equations of gas dynamics in Lagrangian representation have been developed for modeling one-dimensional hydrodynamic processes in the near zone of explosion. The described model has shown its working efficiency within a wide range of explosion energies and environmental conditions. (C) 2010 Published by Elsevier Ltd.