The objective of this work is to develop mechanical design for biomimetic underwater vehicle. The aim in future is to construct vehicle prototypes with propulsion mechanisms with the lowest possible complexity by using vibrations and shockwaves. Such mechanical design can be than used to produce various gait patterns in response to various hydrodynamic events. This paper considers dynamics of a console beam (approximate model of robot fish tail with caudal fin) while moving the contact point with a hull (applicable for any law of motion). In our research we assume that medium resistance is linearly dependent on velocity, and the bending form of elastic line of a tail is set in advance. Simplified differential equations of system's movement are generated and approximate solution for engineering calculations is offered.