The seakeeping properties of a LNG carrier in waves with partially filled tanks are influenced by the flow inside the tanks. The LNG carrier at relatively calm water could induce large movement of the fluid in the tanks and lead to sloshing inside them. The flow inside tanks may generate large forces and moments which depends on the tank size, its geometry and filling ratio. Investigations of coupling effects between ship motions and sloshing can be carried out analytically, numerically and experimentally, depending on the aim of the study. Numerical investigations of ship motions, sloshing and also their coupling effects are common practice.</br> To achieve an accurate prediction of the interaction of sloshing and ship motions, complex numerical models, considering nonlinearities related to both sloshing and seakeeping, need to be developed. To deal with these challenges, this work contributed to improve numerical techniques as well as mathematical models of key physical phenomena. This research work was concerned with the development and validation of CFD method for predicting sloshing inside partially filled tanks and its effects on ship motions.</br> Field method and hybrid method, which, based on the open source tool libraries OpenFOAM, were further developed, validated and utilised. Field method for solving incompressible and compressible free surface Newtonian flows using Reynolds averaged Navier-Stokes equations was adopted in sloshing simulations. The compressible VoF method was extended with the generic wave generation and the absorption method for coupled ship motions with sloshing simulations. Hybrid method followed by coupling a Rankine source time domain solver for ship motions in waves with the RANS based field method for liquid sloshing in partially filled tanks. To estimate the influence of spatial and temporal discretisation, sensitivity studies were conducted for the investigated cases.</br> Investigation cases are: a test tank under well defined single impact wave motions; a large tanker KVLCC2, a post-Panamax containership DTC and a mediumsize cruise ship, with different ship speeds in various wave conditions; a LNG carrier with and without partially filled tanks at zero speed in regular head and beam waves. Comparative available experimental model test measurements of sloshing, ship response and their coupling effects validated the numerical methods.</br> Results demonstrated that 1) it was necessary to account for compressibility to ensure an accurate representation of sloshing flow dynamics; 2) sloshing in partially filled tanks influenced ship motions and, therefore, should be accounted for when simulating the seakeeping behavior of LNG carriers. This was especially valid for surge motions in head seas and roll motions in beam seas.