In this paper, dynamic modeling and parametric study of a vibration-driven robot with planar motion are investigated. The considered robot consists of a main rigid body and two moving masses which move in two directions perpendicular to each other to make a planar motion. By changing the vibration amplitude and excitation frequency of the moving masses, different motion maneuvers are created for the vibration robot. At first, the dynamic equations governing the motion of the vibration robot are derived by considering the dry Coulomb friction for the stick-slip phenomenon and using the Lagrange method. Then, the employed numerical solution of the equations is compared and validated by the Simscape results. Then, the effect of various parameters such as amplitude, frequency, and phase difference between two moving masses on the average longitudinal, lateral and rotational velocity of the vibration robot is investigated. In the end, a discussion and conclusions are presented.