The motion of a rigid particle suspended in two-dimensional flow through bifurcations of diverging microvessels (DMs), and converging microvessels (CMs) is dependent on multiple complex factors that include the geometry of the network, the angle of the bifurcation, the pressure gradient across the microvessel, the geometry of the cells and their radial location in the vessels. To determine how these parameters affect cell trajectories and flux into downstream branches of CMs and DMs, the motion of cells flowing into a DMs and CMs bifurcation, with a 45 degrees branch angle has been modelled, for every location by means of the finite-difference analysis (FDA). The modeling data was compared with direct experimental data from converging and diverging microvessels obtained from mesenteric microcirculation of the rat. Detailed statistical analysis showed significant correlation between the modeling data and experimental data. This model provides estimates of RBC flow along the trajectory path through bifurcations of CMs and DMs; sites which may be crucial for flow stoppage, depending on the vessel diameter and cell deformability.