The present study investigates flow dynamics between two dimensional compliant plates under sinusoidal flow conditions in order to understand influence of wall motion, impedance phase angle (time delay between pressure and flow waveforms), and non-Newtonian fluid on wall shear stress using computational fluid dynamics. The results showed that wall motion induced additional terms in the streamwise velocity profile and the pressure gradient. These additional terms due to wall motion reduced the amplitude of wall shear stress and also changed the mean wall shear stress. The trend of the changes was very different depending on the impedance phase angle. As the impedance phase angle was changed to more negative values, the mean wall shear stress decreased while the amplitude of wall shear stress increased. As the phase angle was reduced from 0°to -90°under $pm$4% wall motion, the mean wall shear stress decreased by 12% and the amplitude of wall shear stress increased by 9%. Therefore, for hypertensive patients who have large negative phase angles, the ratio of amplitude and mean of the wall shear stress is raised resulting in a more vulnerable state to atherosclerosis according to the low and oscillatory shear stress theory. We also found that non-Newtonian characteristics of the blood protect atherosclerosis by decreasing the oscillatory shear index.