Extreme waves significantly affect the coastal structures, activities, and population. Therefore, investigation of extreme wave impact on coastal regions is essential. In this study, a mathematical model is presented to analyse the impact of transient long waves on coastal structures. The mathematical model is constructed based on the Boussinesq equation (BE) with variable water depth including dispersion properties. The numerical solution of BE is constructed by using FEM. The present numerical model is validated through the existing study of Lepelletier (1981) and convergence analysis is also conducted to determine the convergence rate. The present FEM model is implemented on realistic Paradip port, Odisha, India to determine the wave amplitude at various record stations. In addition, the impact of incident waves with angular variation is analysed in the Paradip port. The causes and countermeasures have been proposed based on the simulation results to improve the resonance in the port.