Arterial stenoses may cause critical blood flow and wall conditions leading to clinical complications. In this paper computational models of stenotic carotid arteries are proposed and the vessel wall collapse phenomenon is studied. The models are based on fluid-structure interactions (FSI) between blood and the arterial walls. Coupled finite element and computational fluid dynamics methods are used to simultaneously solve for stress and displacement in the solid, and for pressure, velocity and shear stress in the fluid domain. Results show high wall shear stress at the stenosis throat and low (negative) values accompanied by disturbed flow patterns downstream of the stenosis. The wall circumferential stress varies abruptly from tensile to compressive along the stenosis with high stress concentration on the plaque shoulders showing regions of possible plaque rupture. Wall compression and collapse are observed for severe cases. Post-stenotic collapse of the arterial wall occurs for stenotic severity as low as 50%, with the assumption that a given amount of blood flow needs to pass the stenotic artery; whereas if constant pressure drop should be maintained across a constriction, then collapse happens at severity of 75% and above. The former assumption is based on the requirement of adequate blood supply to the downstream organs/tissue, while the latter stems from the fact that the pumping mechanism of the body has a limited capacity in regulating blood pressure, in case a stenosis appears in the vasculature.