Global natural gas resources are growing and are increasingly geographically diverse. A Floating Storage and Regasification Unit (FSRU) is one of the most commonly used vessel types in the global ship fleet due to the possibility of storage, reloading to another ship, and regasifying it for re-injection into the natural gas grid. It is important to control system parameters for reliable technological processes such as tank hydrostatic pressure, vapor pressure, LNG density, LNG temperature, and phase changes between liquid and gas states. Additionally, pressure monitoring is important to control during transit in port and bunkering to prevent the pressure in the tanks from exceeding the tank design pressure. In this research study, a comprehensive hydrodynamic model for an LNG storage tank in a real-life regasification terminal (Floating Storage and Regasification Unit, LNG Terminal of Klaipeda City, Lithuania), operating in transportation mode to the regasification unit, was created. For this research, LNG is investigated as a compressible liquid and the speed of sound in LNG is evaluated. A complex mathematical model of the system allows the analysis of high-speed hydrodynamic and dynamic processes at cryogenic temperature (110 K) and evaluates the geometric parameters (tank geometry, electric motors and pumps, pipe geometric parameters, and roughness of internal surfaces) and the characteristics of pumps and electric motors. The complex mathematical model of the system was implemented using Fortran programing language and MATLAB R28a. It determined the parameters (pressure, velocity, liquid level of LNG in the tanks, electric motor angular velocity, torques, hydraulic energy losses, etc.) of the system during its start-up mode (until 5 s). It was found that hydraulic energy losses in all pipes contain 1.7% of the whole system power (the total power of the electric motors is 3132 kW). In case of increasing energy costs, this model could be used to control energy losses during the operation of the FSRU in various technological modes.