The aim of this work is the development and study of a mathematical model of the floating dock initial stability for solving problems of list and trim stabilization. The proposed model allows calculating the change of the parameters of the initial stability of the floating dock (with and without a vessel) for different values of the draft. The initial stability of the real floating dock of the middle class with a carrying capacity of 8500 tons is studied using the simulation model developed by the authors in the FREE!SHIP Plus. With the help of this computational model, the operation of immersion of the floating dock is considered. At each stage of immersion at a certain draft, the parameters of the initial stability of the floating dock are calculated, namely, the values: transverse and longitudinal metacentric heights, centers of buoyancy, centers of gravity, and mass displacement. Corrections of transverse and longitudinal metacentric heights due to changes in the mass of liquid in ballast tanks and the influence of its free surface are also taken into account. Based on the obtained modeling results, the following dependences are calculated: a) moments from list and trim angles at different values of draft, b) moments of list and trim from draft at various values of list and trim, c) angles of list and trim from the fill level of the respective tanks. These dependences can be used for further development of the list and trim stabilization system for the given floating dock.