Due to the lack of information about the concept of Tons of Steering Pull (TSP) of many escort tugs, and the lack of research works relating the TSP demanded by a tethered vessel with respect to the TSP provided by tugs, the present paper shows an original study with mathematical models on how to solve these problems. What is more, an important percentage of the towing sector always employs Bollard Pull (BP), which is considered the only parameter capable of defining performance, so this paper aims to relate BP with TSP. The present research was carried out based on more than 25 escort tugs of different towing companies. Furthermore, a real case study of different tanker vessels was used for modelling purposes of tethered vessels’ TSP. Finally, once the proposed models were obtained, they were compared with International Maritime Organization (IMO) guidelines. The results showed charts with the main independent variables of tugs and vessels in order to be as useful and practical as possible to the shipping industry, mainly to ship owners and tug operators, from a safety point of view.