Fatty streaks and fibrous plaques are known to be localized in bends, junctions, and branches of the large arteries, suggesting a significant role for fluid mechanics in the genesis of arterial disease. Various mechanisms have been proposed in the literature based on the known occurrence of eddies and high surface traction. For the purpose of helping in the evaluation of these mechanisms, the flow behavior in a bifurcation was chosen for study. The equations of continuity and motion were solved using the marker and cell numerical technique for the two-dimensional, periodic flow of a Newtonian fluid through a horizontal, bifurcating, rigid channel. Both regions of eddying at the outer wall and of high shear stress at the inner wall were shown by the calculations for both steady and pulsatile flows. The eddies disappeared completely during a portion of each cycle for pulsatile flow.