Soft pneumatic actuators with pleated structures inherently have many advantages, such as low input pressure, high bending speed, and large-amplitude motion, which make them have great potential in the fields of fragile items, medical rehabilitation, and auxiliary assistance. However, modeling and predicting their behavior is a challenge for many researchers due to the discontinuity of pleated structures and the nonlinearity of materials. In this paper, to predict the bending angle and the tip contact force of the soft actuator, several discrete chambers are equivalent to a single chamber within a continuum actuator by using the constant volume principle of elastomer material. On this basis, an analytical model is proposed by introducing the Neo-Hookean hyperelasticity theory, which can derive the relationships of tip contact force of the soft actuator, input pressure, and bending angle. In order to verify the proposed model, seven pleated soft pneumatic actuators with different specifications (actuator length L0, distance between adjacent chambers Ls2, top wall thickness t) are designed and made. And the effectiveness of the proposed model is investigated by multiple physical experiments and finite element method (FEM) simulations. Furthermore, the experimental study shows that the final results successfully demonstrate that the proposed analytical model can predict the bending angle and the tip contact force of the soft actuators well.