A new piezoelectric inchworm actuator with screw clamping mechanisms has been developed recently for the wing folding mechanism of a small unmanned aircraft where the actuator power density is a great concern. Considering that the prototype actuator was designed just with engineering intuition and the performance optimization through experimental developments would take a vast amount of cost and time, a mathematical model was developed to investigate the actuator's critical design parameters and optimize its presently undesirable performance. Based on the lumped parameter method reported previously, and taking full account of the detailed modeling of the complex actuator housing and the actual nonlinear behaviors from the high-force contact and friction occurring at the screw-nut interface, as well as the output performance of the main drive elements including the piezoelectric stack and hollow ultrasonic motors (HUSMs), this model was built and then was experimentally verified for its accuracy and availability. Finally, nine design parameters were studied for their individual effect on the actuator's output using the proposed model. The simulation results indicate that the performance can be considerably improved by performing a slight modification to the prototype, and the dynamic modeling and parameter optimization methods used in this study can also serve as a useful reference for the design of similar piezoelectric inchworm actuators with intermittent clamping behaviors.