Abstract. Many experimental and numerical studies have been achieved to describe the transition process of deflagration to detonation when a projectile impacts an explosive. Also a large work has been done for the determination of various parameters -such as the impact pressure, the efficiency factors, etc. of the laser -material interaction. When a laser beam impacts an explosive, the p2~. criterion, characteristic of shock initiated detonations, is no longer valid due to the generated hot plasma whose effect is to decrease the DDT (Deflagration to Detonation Transition) duration. The present paper deals with a modelling of the plasmaexplosive medium allowing the determination of distances and times of the DDT process. The two phase modelling of the granular explosive takes into account the creation of hot spots. The pressure of the plasma is computed using a semi empirical model, while the temperature is obtained from Maxwell Boltzmann statistics. The authors focused their attention on the equation of state for the detonation products and the numerical process.