Soft actuators have allowed for a variety of innovative applications, however, the mathematical modeling of soft actuators is still in its infancy. In this paper, we present a multi-cavity composite soft pneumatic actuator constitutes of multiple layers with embedded multiple air channels. The principle of operation of this actuator is comprehensively analyzed and described through building the analytical model of the actuator with explicit relationships between input pressure and actuator bending angle. We experimentally verify the analytical model of the multi-cavity composite soft pneumatic actuator and finally demonstrated its validity. Such an establishment of theoretical model is of great significance for the design of multi-cavity composite soft pneumatic actuator and their performance prediction in the future.