Recent developments in Computational Fluid Dynamics (CFD) enabled common access for researchers and thus offers solutions to various complex problems in many different fields. With this motivation, in this study, two kinds of numerical methods were employed to investigate the vertical motions in variable regular waves. While the potential method is commonly known as linear "strip theory", the viscous approach is (the state of the art) named as URANS (Unsteady Reynolds Averaged Navier Stokes) solver which has a fully non-linear base. The DTMB 5415 ship model form was selected for a series of computational work. A numerical study was carried out to understand the seakeeping behaviour of the displacement hull for the stationary case Fn=0 and a high speed case Fn=0.41. The RAO (Response Amplitude Operator) graphs for the coupled heave - pitch motions and the ship's vertical accelerations were generated for five encounter frequencies. The numerical results obtained were validated with the existing experimental data and comparisons were made between the two numerical approaches with the help of RAO graphs. The obtained results showed that the limitations of the strip theory pose a handicap as the assumptions involved in the theory narrow down its application. The nonlinear viscous URANS approach tends to be a better option returning closer results to experiments in a wide Froude number range but on the other hand it does not possess the practicality of the strip theory.