In this paper, we considered the pulsatile flow of blood through catheterized tapered artery in the presence of an ω-shaped stenosis. Blood flow is modelled as homogeneous incompressible couple stress fluid. Further the effects of velocity slip at the arterial wall are also examined. The analysis is carried out analytically and closed form solutions are obtained with the assumption of mild stenosis. In the present study, we analyze the effects of various fluid and geometric parameters on the physiological parameters such as resistance to flow and shear stress at the wall. The variation in the resistance to the flow and wall shear stress with respect to stenosis size (∊,ψ), radius of the catheter (Rc), couple stress fluid parameters (β,ω), Reynolds number (Re) and pulsatile parameter (σ) has been studied. In particular shear stress at the wall is reckoned at both the locations corresponding to the maximum height of the stenosis. It has been observed that this physiological parameter is independent of the location of the maximum height in case of nontapered artery while these locations significantly impact the shear stress at the wall in case of tapered artery. The locations of the critical and maximum heights with corresponding annular radii are summarized in the form of Table 1. We also focussed our attention on the analysis of the wall shear stress over the entire stenosis region for various values of the geometric and fluid parameters. It is observed that the impedance and wall shear stress are increasing with increase in the radius of catheter and stenosis size while they are decreasing as the tapered parameter and the couple stress fluid parameters are increasing. It is observed that slip velocity and diverging tapered artery facilitate the fluid flow.