A theoretical model is built in this study for analyzing and predicting the deformation of a bending-type soft pneumatic actuator used for bionic robotic fish. The actuator is composed of two symmetrically distributed silicone rubber blocks (Ecoflex0030 from Smooth-on Co., Ltd.). Between the two rubber blocks, an ABS plate is fixed to work as a neutral layer. When one side of the actuator is inflated, it consequently bends toward the uninflated side. The deformation of the actuator on the inflated side and the uninflated side, respectively, is analyzed based on principles of elasticity mechanics. The deformation on the inflated side is simplified to planar type and is decomposed into two mutually perpendicular directions to analyze the stress state. A two-step deforming process is proposed to study the stress state on the uninflated side. The two components are combined to determine the relationship between the bending angle of the actuator and the actuating pressure. The proposed model is compared with a finite element analysis model in which the same constraint, load, and materials are used. An experiment under the same conditions was implemented to validate the model. The experiment demonstrates that the accuracy of the theoretical model is adequate to indicate the response of the soft pneumatic actuator to the actuating pressure. A bionic fishtail system based on the soft pneumatic actuator was also established to verify the applicability of the actuator to bionic robotic fish.