The approach angle of a cyclone in a coastal location plays a significant role while considering the worst-case surge scenarios for coastal vulnerability studies. The study focuses on the sensitivity of the approach angle on the tide surge interaction in a narrow continental shelf and concave coastal geometry. To study the storm surge hydrodynamics, we have performed simulations using the Advanced Circulation (ADCIRC) model considering ‘Thane’ cyclone by varying its angle of approach. We investigated the variability in the storm surge behaviour within the concave coast by computing the net flux movement. The highest surge amplitudes and highest storm tide occurred at an inflexion point and their magnitude varied based on the proximity of the cyclone track to the shore. We found that, at the landfall point the maximum surge height is for an approach angle of 75° then for 105°, and the least for 45°. The study also shows that the peak surge attributes under go a higher variability inside a concave coast, even for those cyclone tracks on a similar shelf width and slopes. A statistically highly significant positive correlation exists between the flux movement inside the concave coast and the surge height.