Based on the nonlinear geometric relationship of the bulging angle and the bending angle, and the principle of virtual work and nonlinear constitutive relationship of Neo-Hookean incompressible hyperelastic material, a quasi-static mechanical model for pneumatic toothed soft actuator was established, considering the strain energy of the bottom, side walls, and front and rear walls. Considering the geometric nonlinearity and material nonlinearity, the proposed model could solve the configuration of the soft actuator at different driving pressures and terminal loads precisely and efficiently. The finite element simulation of the cantilevered-free soft actuator was conducted by Abaqus, and the corresponding experimental device was established. The simulation analysis and experimental investigation were performed at different driving pressures. A comparison of the results show that there is a positive linear correlation between the driving pressure and the bending angle of the soft actuator, and the prediction of the theoretical model agrees well with the simulation and experimental results. In addition, the distribution of the strain energy was analyzed. Based on the equal-curvature model, the configuration results of the soft actuator at terminal loads are basically consistent with those obtained by Abaqus. The proposed quasi-static mechanical modeling method provides a theoretical basis for the structural optimization design, performance improvement, and motion control of similar soft actuators.