The periodicity of the physiological flow has been the major interest of analytic research in this field up to now Among the mechanical forces stimulating the biochemical reaction of endothelial cells on the wall, the wall shear stresses show the strongest effect to the biochemical product. The objective of present study is to find the effects of velocity waveform on the wall shear stresses and pressure distribution along the artery and to present some correlation of the velocity waveform with the clinical observations. In order to investigate the complex flow phenomena in the bifurcated tube, constitutive equations, which are suitable to describe the rheological properties of the non-Newtonian fluids, are determined, and pulsatile momemtum equations are solved by the finite volume prediction. The results show that pressure and wall shear stresses are related to the velocity waveform of the physiological flow and the blood viscosity. And the variational tendency of the wall shear stresses along the flow direction is very similar to the applied sinusoidal and physiological velocity waveforms, but the stress values are quite different depending on the local region. Under the sinusoidal velocity waveform, a Newtonian fluid and blood show big differences in velocity. pressure, and wall shear stress as a function of time, but the differences under the physiological velocity waveform are negligibly small.