Abstract. The JWL EOS is widely used in different forms (two, three terms) according to the level of accuracy in the pressure-volume domain that applications need. The foundations of the relationship chosen to represent the reference curve, Chapman-Jouguet (CJ) isentrope, can be found assuming that the DP expansion isentrope issued from the CJ point is very nearly coincident with the Crussard curve in the pressure-material velocity plane. Its mathematical expression, using an appropriate relationship between shock velocity and material velocity leads to the exponential terms of the JWL EOS. It well validates the pressure-volume relationship chosen to represent the reference curves for DP. Nevertheless, the assumption of constant Gruneisen coefficient and heat capacity in the EOS thermal part remains the more restrictive assumption. A new derivation of JWL EOS is proposed, using a less restrictive assumption for the Gruneisen coefficient suggested by W.C. Davis to represent both large expansions and near-CJ states.