Recently, tug boats are widely used for towing a barge which transports building materials, a large block of a ship, offshore crane, and so on. In order to simulate the dynamics of the coupled towing system correctly, the dynamics of the towline should be well modeled. In this paper, the towline was modeled as the multiple finite elements, and each element was assumed as a rigid cylinder which moves in five degrees of freedom except roll. The external tension and its moment acting on each element of the towline were modeled depending on the position vector's direction. Tugboat's motion was simulated in six degrees of freedom where wave and current effects were included, and towed barge was assumed to move in the horizontal plane only. In order to confirm the mathematical models of the coupled towing systems, standard maneuvering trials such as course changing maneuver, turning circle test and zig-zag test were simulated. In addition, the same trials were simulated when the external disturbances like wave and current exist. As the result, it is supposed that the results might be qualitatively reasonable.