In Heavy Marine Transport, it is common practice to drytransport large and heavy floating offshore structures. In general, loading and discharge of these floating cargoes on- and from heavy transport vessels is done at sheltered locations, like harbors, where sea-state and swell conditions are insignificant. Often these locations are at large distance from operating fields of the offshore structures, which means that the structures need to be towed from- or to these fields. To save time and costs, it is beneficial to perform the loading and discharge operations in the field. This necessitates a reconsideration of the maximum allowable wave conditions such as to perform the loading- and discharge operations within specified time frame whilst ensuring safety of crew, cargo and heavy transport vessel. Therefore accurate prediction tools to determine the relative motions between heavy transport vessel and cargo are required. In the past, studies have shown that standard prediction tools over-estimate relative vertical motions compared to model tests and practical experience. This paper discusses the prediction of relative vertical motion, which is dominated by the phenomenon squeeze flow. From model tests and CFD calculations non-linear hydrodynamic loads related to squeeze flow are recognized. Standard linearized solutions do not cover the non-linear loads and therefore result in a lack of accuracy in predicting the relative vertical motions. Linearized solutions assume small motion amplitudes with respect to characteristic dimensions of the flow problem; in the case of squeeze flow this assumption is not valid as the motion amplitude may be in the same order as the gap between cargo bottom and the deck of the heavy transport vessel. With linearized potential solvers it is found that the added mass is strongly dependent on the gap height, which verifies the analytical work of Molin et al. . Following the work of Molin, the change in added mass due to changing gap height gives a large contribution to the non-linear hydrodynamic load. Additionally, a second important contribution is related to the relative vertical velocity, recognized as a drag component. As such, a non-linear formulation is found which can be used in a time-domain approach. This formulation requires gap-height dependent added mass as found using the linearized potential solver. As potential solvers are known to have difficulty dealing with the small gap, different methods have been investigated. Results of model tests and CFD calculations are shown, which are used to tune the non-linear formulation. Tuning is done by adapting the drag component. Furthermore, results of a multi-body problem based on standard linear hydrodynamics and the non-linear formulation are compared.