This paper deals with the attitude control of a towfish (underwater towed vehicle) with two elevators and a single rudder to improve the image quality of an attached sound navigation ranging (sonar) system. Image distortion can occur if the towfish shakes excessively. Since a towfish is connected to the mother ship through a towing cable and the motion of the towfish is affected not only by the motion of the cable, but also by the position of the center of gravity, towing point, and towing speed, it is necessary to analyze how these factors affect the towfish to appropriately control its attitude. In this study, a method for obtaining a feasible region of the towing point in accordance with the variations in the center of gravity and towing speed is proposed, and the feasible region obtained can ensure that pitch control can be achieved using the installed elevators. In addition, the allowable range of disturbances for yaw control was also investigated. Simulations were conducted using the dynamic models of the towfish and cable to check the obtained feasible region/range, and it was confirmed that there is a region/range where the attitude control can be carried out with relative ease.