The primary goal of this research is to develop a three-term mesoscopic reaction rate model that consists of a hot-spot ignition, a low-pressure slow burning and a high-pressure fast reactionterms for shock initiation of multi-component Plastic Bonded Explosives (PBX). Thereinto, based on the DZK hot-spot model for a single-component PBX explosive, the hot-spot ignition term as well as its reaction rate is obtained through a "mixing rule" of the explosive components; new expressions for both the low-pressure slow burning term and the high-pressure fast reaction term are also obtained by establishing the relationships between the reaction rate of the multi-component PBX explosive and that of its explosive components, based on the low-pressure slow burning term and the high-pressure fast reaction term of a mesoscopic reaction rate model. Furthermore, for verification, the new reaction rate model is incorporated into the DYNA2D code to simulate numerically the shock initiation process of the PBXCO3 and the PBXC10 multi component PBX explosives, and the numerical results of the pressure histories at different Lagrange locations in explosive are found to be in good agreements with previous experimental data. (C) 2016 Elsevier B.V. All rights reserved.