Fish-like swimming has been attracting scientists and engineers attention since many years resulting in attempts of mathematical description of fish movement and its implementation in many interesting prototypes of underwater vehicles. In this paper, conception of research on simulation, implementation and control of bionic underwater vehicle BUV with undulating propulsion is presented. In the next sections, introduction and mathematical model of bionic underwater vehicle motion are included. Then, the last implementation of the robotic fish called CyberFish, which movement is based on the presented mathematic description is presented and shortly described. In the last sections, conception of research on control system of BUV and conclusions are presented.