Pressure cartridge type separation devices which are widely used in fairing, stage separations of space launch systems, and many other aerospace fields generate much lower pyroshock and produce no high-speed debris compared to frangible explosive separation devices. However, because the operation is completed in a few milliseconds and the releasing mechanism is complicated, their separation behavior is difficult to experimentally identify. This paper presents a mathematical model to simulate the separation behaviors for a split-type separation bolt, one of the pressure cartridge type separation devices. The mathematical model includes a combustion model, buckling resisting model, split behavior model related to static and dynamic friction, O-ring friction model, contact force model, and slip angle model. Each composing models are obtained by mathematical formulation or numerical analysis. An efficient contact model is constructed by using virtual penetration model appropriately for complex contact phenomenon. To validate the established model, separation experiments were performed; the results are then compared with the mathematical model. Present study show that complex mechanical behaviors coupled with combustion of solid propellant charge can be efficiently simulated by the mathematical model.