<p>Tsunami induced wave propagation with varying heights towards any coastal area depends significantly on the bathymetry of the adjacent shelf region. Based on the theory of shallow water waves, numerical simulation has been carried out in the present study with linear and nonlinear shallow water models in one-dimension (1-D) using finite difference method (FDM) selecting six different coastal stations of eastern India adjacent to north-west Bay of Bengal, namely – (a) Bakkhali and (b) Digha in West Bengal; (c) Chandipur, (d) Paradip and (e) Puri in Odisha; and (f) Visakhapatnam in Andhra Pradesh. Some initial tsunami-like disturbance has been assumed for performing the simulation with both the linear and nonlinear 1-D shallow water models incorporating the off-coast bathymetry adjacent to the selected stations. The velocity attained by the waves propagating toward the coast at a particular depth and time using both models has been computed. Time series analysis is also presented for Digha and Puri coastal stations using both linear and nonlinear models for up to four hours. For simulation, MATLAB code has been developed and real bathymetry data has been obtained from GEBCO for both models. Comparative results of wave height obtained with both linear and nonlinear models are presented. In shallow water regions (depth less than 50&#xa0;m) wave propagation nature could be more realistically understood using nonlinear model according to the study.</p>