Response of shock initiation of cast TNT charges with double-shell casing impacted by hypervelocity fragment was studied using the non-linear dynamics software AUTODYN. The purpose of the study is to gain insight into the physical phenomena underlying debris cloud impacts, and to develop an equation that predicts critical fragment velocity at which a fragment must travel to cause initiation. First, strength model, reaction rate equation and equation of state of materials are briefly described. Second, the threshold law of shock-induced initiation of cast TNT with double-shell casings was obtained by analyzing pressure of the growth process. Final, the threshold shock initiation velocity of the fragment is calculated under different fragment diameter. Based upon above data we modified empirical Jacobs-Roslund model, which is very helpful to guide the safety study on shell charges structure.