A new theoretical mechanical model was proposed by the study, which takes into account ultrasonic vibrations and undeformed cutting thickness. By analyzing the kinematic characteristics of ultrasonic vibration, the undeformed cutting thickness under ultrasonic vibration drilling is calculated, and the theoretical analysis of axial forces and torques is carried out by using the model with simulation software. The results show that both the theoretical drilling force model and the 3D drilling simulation can predict the average axial force and average torque of SiCp/Al composite drilling process more accurately, and the simulation prediction results are better than the prediction results of the theoretical model. The average error of the simulated axial force is 7.11% and the average error of the torque is 7.19%, and the average error of the theoretical axial force is 10.49% and the average error of the torque is 13.05%.