In this paper, a new method for fracture analysis of notched cylindrical cases under explosive loading of High Explosive internal charge has been presented to determine fracture time, fracture radius, fragment velocity and acceleration. Also the fracture dynamics has been simulated by explicit and nonlinear LS-DYNA code. In numerical simulation the behaviour of metallic case has been modeled by JOHNSON-COOK model, and of HE charge by HIGH-EXPLOSIVE-BURN. Mie-Gruneisen and JWL equations of state have been used for the materials. Finally, the results of the analytical model, the numerical simulation and extended Taylor's model have been compared, and the effects of some paremeters on the fracture time, fragment velocity, and expansion radius have been discussed .