The aim of the work is mathematical description and simulation of an underwater robot, which is meant for cleaning off the outgrowth from ship hulls. The task of mathematical simulation involves defining in differential terms all the variables considered: driving torque of the DC motors used for driving the caterpillars, which is a function of motor current and, consequently, input voltage; inertial characteristics of the robot; frictional and environmental resistance forces, out of which resultant motion parameters - position, velocity and acceleration - of the robot can be expressed.