The transformation of waves is one of the important subjects in coastal engineering studies. Refraction, diffraction, shoaling, reflection can be analysed with the mild slope equation over mild sloped topographies. But the extended mild slope equation can be applied to the rapidly varying topographies since it includes higher order bottom effects such as square of bottom slope and bottom curvature. In this study, extended mild slope equation has been solved with finite difference method using Mac Cormack and Point Gauss Seidel Methods together. The nonlinear wave celerity and group velocity have been used. The numerical model has been tested on elliptic shoaling area and compared with the physical experiment measurements given in literature. The predictions are in consistency with the measurements. As a result of error analysis, it is decided that the numerical can be used for the simulation of wave propagation. Numerical model has been applied to a coastal area in the Kocaeli Bay in the Marmara Sea in Turkey.