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The article provides a review and analysis of mathematical models of the movement of a vessel, which is controlled by one or two rudder propellers, and the main tasks that are solved using these models. It has been pointed out that there are a sufficient number of mathematical models that describe the movement of a vessel equipped with a classical control scheme of propulsion: rudder - screw propeller. Such models are not applicable to the type of vessel under consideration. Since the ship is represented as a dynamic system with six degrees of freedom, which is affected by complex changing external conditions (wind, waves, etc.), then the ship’s control systems mainly use non-linear models, the construction of which, as well as their use is very difficult, due to their complexity and the small number of studies. To simplify the solution of problems related to the control of the vessel, it is promising to consider the movement of the vessel as plane-parallel. Thus, partial linearization of the model can be achieved by breaking the motion into two components: progressive and rotary motion, as well as using linear models for each part.