This paper is concerned with the formulation and simplifications of the general fluid structure interaction analysis for an advancing oscillating vessel in waves to provide alternative 3D hydrodynamic models to determine first and second-order wave-induced fluid loadings, and, hence, the prediction of low-frequency wave damping coefficients. Heuristic arguments which lead to the Added Resistance Gradient (ARG) method of calculating low-frequency damping coefficients together with two 3D-based calculation procedures are presented. Predictions of added resistance and motion responses are compared with other published data. The intermediate hydrodynamic coefficient predictions based on 2D and 3D hydrodynamic models are compared. Low-frequency damping coefficient predictions based on the two proposed 3D calculation procedures are compared with experimental measurements and earlier published generalized strip theory values. Assessment of the applicability of the procedures, the result of their application, and further possible generalizations of the methods are discussed.