Ensuring navigational safety of a vessel entails the determination of the manoeuvring coefficients or the hydrodynamic derivatives and the subsequent simulation of its trajectory well in advance of constructing the ship and this task is indeed a very challenging one. The number of hydrodynamic derivatives to be determined is based on the mathematical model used for the representation of hydrodynamic forces and moments. This chapter presents the mathematical formulation of the problem and the numerical approach used for obtaining the hydrodynamic derivatives. For this, an attempt has been made to numerically simulate the conventional horizontal planar motion mechanism (HPMM) towing tank experiment using the RANSE CFD model. A container ship model has been modelled for performing simulation andanalysis. The numerical tank size has been set following the ITTC guidelines, applying the grid size of 600,000 hexahedral cells. The free-surface effects have been taken into account. The prescribed body motions have been modelled by using the mesh morphing ANSYS CFX technique with 3-modes motion viz. pure sway, pure yaw and combined sway and yaw motions, referred as combined motions in this chapter. The time histories of forces and moments have been approximated with the Fourier series in order to enable the comparison with the corresponding equations for forces and moments, as represented by the developed mathematical model defined with linear and non-linear hydrodynamic derivatives. These computed derivatives have been compared with the experimental results, showing reasonably good agreement. © 2020, Springer Nature Switzerland AG.