In order to solve the stress concentration problem of the extension and bending deformation of the stacked PZT (Pb(Zr, Ti)O₃) actuator used in piezoelectric fast steering mirror (PFSM), the extension and bending deformation model of the stacked PZT actuator was analyzed firstly based on Timoshenko model. Then, the relationships between the dynamic stress of stacked PZT actuator and the driving voltage amplitude, the driving voltage frequency and bending stiffness of flexible hinge on top of PZT actuator were analyzed by the method of piezoelectric coupling theory. Finally, the optimal design parameters of 300 mm diameter PFSM were obtained by response surface method. The research method and analysis results of this paper could provide reference for optimizing the parameters of key components of PFSM, reducing the stress concentration of stacked PZT actuator, and improving the durability and reliability of PFSM.