Problem statement. Mobile robotic systems are widely used in various fields of industry and social life: from small household appliances to large-size road-building machinery. Specific attention of scientists and designers is paid to the vibration-driven locomotion systems able to move in the environments where the use of classical wheeled and caterpillar robots is impossible or inefficient. Purpose. The main objective of this paper consists in generalizing the actual research results dedicated to various design diagrams and mathematical models of suspension systems of mobile vibration-driven robots. Methodology. The differential equations describing the robot motion are derived using the Lagrange - d'Alembert principle. The numerical modeling is carried out in the Mathematica software by solving the derived system of differential equations with the help of the Runge - Kutta methods. The verification of the obtained results is performed by computer simulation of the robot motion in the SolidWorks and MapleSim software. Findings (results). The time dependencies of the basic kinematic parameters (displacement, velocity, acceleration) of the robot's vibratory system are analyzed. The possibilities of maximizing the robot translational velocity are considered. Originality (novelty). The paper generalizes the existent designs and mathematical models of the mobile vibration-driven robots' suspensions and studies the combined four-spring locomotion system moving along a rough horizontal surface. Practical value. The obtained results can be effectively used by researchers and designers of vibration-driven locomotion systems while improving the existent designs and developing the new ones. Scopes of further investigations. While carrying out further investigations on the subject of the paper, it is necessary to solve the problem of optimizing the robot's oscillatory system parameters in order to maximize its translational velocity.