A crane system offers a typical control problem being an under actuated MIMO system. In this paper, the precise modeling of a 2D gantry crane system with 3 DOF is considered. First a simple dynamic model of the system is obtained using Lagrange's equations of motion. Then, friction non-linearities were added to the model, which were found to decrease the output magnitudes from reference values. The model was further improved by considering the possibility of 3D angular swing which showed more accurate transient responses. Finally, the dynamics of hoisting cable flexibility was added to the system resulting in a complex model requiring time consuming simulation.