In order to guarantee safe operations in the offshore industry, at all time it is necessary to predict motion behaviour of structures in specific sea states accurately. Safety is very important for the offshore industry, which can come in jeopardy when motions are either extreme or unexpected with regards to predicted motion behaviour. This thesis aims to establish improved motion behaviour prediction of a barge in shallow water. A parametric model is developed, in both frequency as well as time domain, which contains flexibility for other, non-linear wave theories, as well as other non-linear effects like viscous damping or an additional inertial force which can atone for the approaching seabed in shallow water motions. It utilises hydrodynamic coefficients from the diffraction analysis in ANSYS AQWA, with which motions are also verified. As no validation data were available, this verification was very important. The accuracy of motion prediction is verified in both Frequency Domain (FD) and Time Domain (TD), which assures its applicability. The model subsequently is wider applicable, as it allows for non-linear wave theories or modifications by other external forces. Parameters Ursell Number (UR), steepness S and relative depth μ are defined which determine the validity of wave theories. These parameters display theoretical limits of applicability and validity of the Linear Wave Theory (LWT). The parametric model is capable of calculating associated wave forces up to second order, which can modify the predicted motion behaviour for higher waves than the LWT allows. In the model a Vessel - object and Wave - object are defined. The former is for this thesis a rectangular barge, while the latter contains information on the sea state, defined by input parameters wave height H, wave period T and water depth d. In both FD and TD vertical displacements of four vertices are calculated, based on the heave, roll and pitch Degree of Freedom (DOF). Subsequently, viscous effects are included based on a factor of the critical damping in each specific DOF, which moderates the vertical motion especially near resonance. A numerical example of an additional inertial force to account for cushioning and sticking is elaborated, which displays effects of an approaching seabed on heave displacement. These values are based on water particle velocities in the Under Keel Clearance (UKC), but is not verified nor validated, so no general conclusion can be drawn. It does show nicely how the model is capable of dealing with additional external forces and subsequently calculates resulting motions. Second order effects increase in significance in shallow water of which set - down is an important non-linear shallow water effect, which has great significance in predicting ultimate vertical motions. The numerical solutions for a mono-directional bi-chromatic wave group show that these additional displacements are in such an order of magnitude that it should be accounted for in shallow water ship motion hydrodynamics. Viscous moderations are also within this order, although these exist by the grace of the structure’s velocity, while set - down is a phenomenon related to the waves, which occurs regardless of a vessel present or not.