The present study deals with the influence of time dependent stenosis and slip velocity on blood flow through an arterial segment. The problem is investigated by a joint effort of analytical and numerical techniques. The expressions of wall shear stress, resistance to flow, axial velocity and volumetric flow rate are obtained. The graphical representations have been made to validate the analytical findings with a view of its applicability to stenotic diseases. It is noticed that the resistance to flow and wall shear stress increases with the stenosis height.