The damage of thin steel plate subjected to contact explosions was a very complex nonlinear process. The initial crevasse of plate subjected to contact explosions had influence upon the whole damage process, so the critical damage study was significant on the anti-explosion of ship structure. In virtue of the wave solution of the plate plastic dynamic response and the dynamic fracture theory, the critical blasting charge was derived theoretically when onset of initial circumferential crack namely critical damage happened. And the expression of critical deformation was also obtained. Lastly the results calculated using proposed method was compared with numerical simulation and the experiment in the published literature, which were almost coincided. It could be seen that the present method could perfectly solve the critical damage of thin plate under contact explosions theoretically, and provide references for defensive engineering.