Atherosclerosis is a disease that narrows, thickens, hardens, and restructures a blood vessel due to substantial plaque deposit. The geometric models of the considered stenotic blood flow are three different types of constriction of cross-sectional area of blood vessel; 25%, 50%, and 75% of constriction. The computational model with the fluid-structure interaction is introduced to investigate the wall shear stresses, blood flow field and recirculation zone in the stenotic vessels. The velocity profile in a compliant stenotic artery with various constrictions is subjected to prescribed physiologic waveform. The computational simulations were performed, in which the physiological flow through a compliant axisymmetric stenotic blood vessel was solved using commercial software ADINA 8.4 developed by finite element method. We demonstrated comparisons of the wall shear stress with or without the fluid-structure interaction and their velocity profiles under the physiological flow condition in the compliant stenotic artery. The present results enhance our understanding of the hemodynamic characteristics in a compliant stenotic artery.