The friction drilling process is very important in various industries such as automotive, aerospace, and oil and gas industries. Therefore, they have always sought to find methods to improve this process. One of these methods is to optimize the application of ultrasonic vibrations in the process, and limited research has been done in this regard. The current research aims to investigate the effect of ultrasonic vibrations simultaneously with the parameters of drilling on the friction drilling process to optimize this process with the help of finite element simulation. Due to the nature of the complex transformations of the process, a Coupled Eulerian–Lagrangian model of the process was first created in the Abaqus software. Then, the process simulation was carried out in the presence and absence of ultrasonic vibrations. Rotational speed, feed rate, and amplitude of vibrations are the influencing parameters, and sheet temperature and axial force, and torque applied to the tool are the parameters investigated in this research. The results show that higher rotation speed and lower feed rate lead to a reduction of axial force and torque. Also, the application of ultrasonic vibration reduces up to 50.48% the axial force and up to 46.67% torque, and this reduction is improved by increasing the range of vibrations. The optimal mode was selected After analyzing 12 different modes based on the lowest amount of axial force and torque on the pin. It was found that the ideal mode occurs at a feed rate of 4.23 m/s and a rotation speed of 3000 rpm, with a 20-µm range. These findings and optimizing drilling parameters bring new horizons in material bonding techniques in various industries.