This study investigates the effects of sway and roll excitations on sloshing liquid loads in a tank, using Ansys Fluent software. The model considered in the study is a 1:50 scaled membrane-type tank, based on a KC-1 membrane LNG tank designed by Korea Gas Corporation (KOGAS). The volume of fluid (VOF) method is used to track the free surface inside the tank, and the standard k-ε model is applied to express the turbulent flow of the liquid. To explore the motion of the tank under excitation, a user-defined function (UDF) and a dynamic mesh technique are employed to control the external forces exerted on the tank through its motion. The results, in the form of time series data on the sloshing pressures in the tank under pure sway, roll, and coupled sway-roll, are analysed, with specific ranges for the excitation amplitudes and frequencies. We show that variations in excitation frequency and amplitude significantly influence the sloshing loads. Sloshing loads are found to intensify when the excitation frequency matches the tank’s primary natural frequency, 1.0 ω1′. Furthermore, with coupled sway-roll excitations, the sloshing loads are weakened when the sway and roll are in-phase and are intensified when these are out-of-phase. Fast Fourier transform analysis provides insights into the frequency domain, showing that the dominant frequency is 0.88 Hz and it is approximately equal to the tank’s primary natural frequency, 1.0 ω1′.