Abstract: A hot-spot shock ignition pore-collapse model of double hollow sphere has been developed, in which binder was assumed to undergo one type of rigid-plastic deformation and explosive was assumed undergo one type of elastic-viscoplastic deformation. The space and time distributions of the velocity, strain and temperature of explosion were theoretically calculated. A new expression of reaction rate was obtained for the hot-spot ignition. A two-dimensional hydrocode DYNA2D was used to simulate the shock initiation of PBX-9404, with a reaction rate model containing the new hot-spot ignition term, the slow burning term at low pressure and the high-pressure reaction term. The numerical results show that the developed model can not only describe the influence of explosive particle size and porosity on the shock initiation, but also can explain the influence of binder strength in PBX on the shock initiation.