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Both finite-element and finite-difference numerical models are applied to simulate storm surges and associated currents generated by tropical cyclones that struck the coast of Andhra Pradesh, located on the east coast of India. During a cyclone, the total water level at any location on the coast is made up of the storm surge, surge-wind wave interaction and the tide. The advanced circulation two-dimensional depth-integrated (ADCIRC-2DDI) model based on finite-element formulation and the two-dimensional finite-difference model of storm surges developed at IIT Delhi, hereafter referred as IITD storm surge model, are used. These models are driven by astronomical tides at the open ocean boundary and cyclonic asymmetric winds over the surface of the computational domain. Comparison of model simulated sea-surface elevations with coarse and finer spatial resolutions suggests that the grid resolution near the coast is very crucial for accurate determination of the surges in addition to the local bathymetry. The model underpredicts surges, and the peak surge location shifts more to the right of the landfall as the spatial resolution of the model becomes coarser. The numerical experiments also demonstrate that the ADCIRC model is robust over the IITD storm surge model for surge computations as the coastline is better represented in the former.