Purpose Carotid artery is often associated with plaque deposition because of its shape and associated flow features. The shape of stenosed bifurcation is characterised by bifurcation angle (ß), planarity angle (α) and severity of stenosis (b). In the present work, three-dimensional numerical computations have been performed to analyse the effect of these geometrical parameters of carotid bifurcation on the characteristics of flow. Design/methodology/approach Governing equations of this study were solved using ANSYS Fluent 20.1 and the blood flow was considered as laminar, pulsatile and non-Newtonian. Instantaneous flow behaviour has been illustrated using vorticity, velocity and helicity contours, whereas the time-averaged wall shear stress ( τw¯) and oscillatory shear index (OSI) quantify the time-averaged behaviour. Findings The recirculation zone and secondary flow are ascertained to be stronger for higher bifurcation angle as compared to the lower bifurcation angle. Strength of the secondary flow is found to reduce with increase in α from 0° to 10°, whereas it grows as α varies from 10° to 20°. For higher bifurcation angles, τw¯ is lower than 2 Pa and OSI is greater than 0.2 on the outer walls. Similar observations were made for τw¯ and OSI distribution on bottom wall in non-planar cases, which predicted atherogenic locations. Originality/value The values for ß were taken as 30°, 45°, 60° and 75°, whereas for α, range of 0°–20° was chosen. The stenosis was considered on the outer wall of internal carotid artery and its severity was considered within the range of 0%–60%.