Abstract: The process of explosives (wrapped coarse granule TNT, =1.547 g/cm3) shock initiation and extinguishment was experimentally investigated and analyzed by Lagrange method in the case of small partition assay. The state equations of explosive and reaction products are all based on JWL state equations. The value-time relations of u,v,e on every Lagrange position are obtained and the parameters in the reaction rate equation have been determined, which utilizies the ignition and growth model.The reaction rate obtained by Lagrange method indicates that there are partly reactions when the shock wave extinguishs in the solid explosives.