In this paper, an improvement has been made to the approximation technique of a complex domain through the stairstep approach to have a considerable accuracy, minimize computational cost, and avoid the hardship of manual work. A novel stair-step representation algorithm is used in this regard, where the entire procedure is carried out through our developed MATLAB routine. Arakawa C-grid is used in our approximation with (1/120)° grid resolution. As a test case, the method is applied to approximate the domain covering the area between 15°–23°N latitudes and 85°–95° E longitudes in the Bay of Bengal. Along with the approximation of the land-sea interface, coastal stations are also identified. Approximated land-sea interfaces and coastal stations are found to be in good agreement with the actual ones based on the similarity index, overlap fraction, and extra fraction criteria. The method can be used for approximating an irregular geometric domain to employ the finite difference method in solving problems related to long waves. As a test case, shallow water equations in Cartesian coordinates are solved on the domain of interest for simulating water levels due to the nonlinear tide-surge interaction associated with the storms April 1991 and AILA, 2009 along the coast of Bangladesh. The same input except for the discretized domain and bathymetry as that of Paul et al. (2016) is used in our simulation. The results are found to be in reasonable agreement with the observed data procured from Bangladesh Inland Water Transport Authority.