The improved design of a vibratory lapping machine is developed in the SolidWorks software on the basis of the suspended double-mass oscillatory system. The system is set into motion by three pairs of electromagnets generating periodic excitation forces applied between the upper lap and the lower one. By adopting the same forced frequencies and the certain phase shifts of the excitation forces, it is planned to provide the antiphase translational (circular) oscillations of the laps. In such a case, the largest accuracy and operational efficiency of the lapping (polishing) process can be reached. The present research is aimed at analyzing the dynamic behavior of the lapping machine’s oscillatory system. In particular, the motion trajectories of the laps, as well as their kinematic characteristics (displacements, velocities, and accelerations) are considered. The mathematical model of the oscillatory system is developed using the Euler-Lagrange equations. The numerical modelling of the system motion is performed in the Mathematica software with the help of the Runge-Kutta methods. The computer simulation of the laps oscillations is conducted in the SolidWorks software under different friction conditions. The experimental prototype of the vibratory lapping machine is implemented in the Vibroengineering Laboratory of Lviv Polytechnic National University. The possibilities of providing the controllable translational (circular) oscillations of laps are theoretically studied and experimentally confirmed. Further investigations on the subject of the present paper can be focused on the physical-mechanical and technological parameters (surface flatness, roughness, hardness, wear resistance, etc.) obtained due to performing the lapping and polishing processes using the proposed vibratory finishing machine.