A mathematical model has been developed to study the theoretical analysis of long waves in a complex geometrical port. The domain of interest is categorized into sub regions and wave functions are evaluated individually in both the regions. Boundary element method is employed to solve the integral equations by utilizing the kinematic and dynamic boundary conditions. The integral equations are further converted into a system of linear equations. The domain is discretized non-uniformly to obtain the optimum accuracy. The solution is obtained by equating the matching conditions at the entrance of the harbor, by using the continuity conditions of the irrotational flow of an incompressible fluid. The theoretical results of the problem obtained from the BEM for the rectangular domain have been verified with studies done by Lee (1971). Based on the validation, the present numerical model is implemented on real domain as Paradip port, Odisha, India for practical applications.