The article is devoted to the study and analysis of the mechanism of undulating propulsion in the case of its application in underwater robots. It gives a brief review of studies related to developing a mathematical model of the movement of an underwater robot. Robot using two-symmetry undulating fin. This mathematical model imitates the movement of some fish species, such as batoid rays. The purpose of the study was to substantiate the possibility of creating a propulsion mechanism. In this mechanism the undulating movement of the fin is provided by individual elements controlled by servomotors. With appropriate control, these movements provide the propagation of the wave in the flexible fin of the robot. The advantage of this approach is a significant increase in the maneuverability of the device compared to existing traditional models. Also, the movement becomes almost silent. The experiments performed on a robot prototype. As a result, a relation is found between the parameters of the undulating movement and the linear speed and thrust of each fin. The parameters of undulating movement such frequency and amplitude are analyzed, to provide stable movement of the underwater robot. The experiments confirmed the possibility of implementing the proposed control method. They Showed the possibilities of controlling the direction of propulsion force by changing oscillating phase of each fin ray. Also, the possibilities of controlling the thrust of the fin by changing the amplitude and frequency of undulating movement of the fin.