To enrich the structure of macro-micro planar motion device, a basin type piezoelectric actuator was proposed in this paper. The 1st order in-plane symmetric bending vibration mode and 2nd order antisymmetric longitudinal vibration mode of the basin type structure were set as the working modes, and the piezoelectric ceramics adhered to the surface of the basin type actuator is used to excite the working modes vibration, forcing the driving feet to travel elliptically along the xOz and yOz planes simultaneously to push the moving bode. According to principle of transfer matrix mechanics, the vibration transfer equation of each element of the actuator is constructed, and by determining transfer conditions between the connecting elements and the piezoelectric boundary, a semi-analytical electromechanical coupling transfer matrix model of the actuator is established, and the solution program of the model was compiled. A multi-objective optimization mathematical model of the actuator was established to obtain its optimal sizes. To validate the semi-analytical model, a finite element model(FEM) of the actuator was also established. The working modal frequency differences obtained from the semi-analytical model and FEM model were 177 Hz and 191 Hz, respectively, and the driving foot’s vibration amplitude along x, y and z directions were 2.95 μm, 3.27 μm, 1.37 μm and 3.12 μm, 3.61 μm and 1.82 μm, respectively, which validated the effectiveness of the semi analytical model. The results indicate that the proposed actuator analysis method combining structural design with driving principles opens up a new idea for optimizing the performance of piezoelectric actuators.