Microvascular transport is strongly influenced by the nonuniform partitioning of red blood cells at diverging microvessel bifurcations, where blood flows from one mother vessel into two daughter vessels. In such bifurcations, the volume fractions of red blood cells in the blood entering each daughter vessel typically differ significantly from the volume fraction in the mother vessel. This phenomenon is caused, to a first approximation, by nonuniform distribution of red blood cells in the cross-section of the mother vessel and the tendency of red blood cells to follow background fluid streamlines. In smaller vessels, however, red blood cell trajectories can deviate significantly from fluid streamlines. In this dissertation, the mechanical reasons for these deviations and their contributions to nonuniform partitioning are analyzed.A two-dimensional model is used to simulate the motion and deformation of flexible particles as they travel alone through a diverging microvessel bifurcation. Deviations of particle trajectories from background fluid streamlines result from migration towards the mother vessel centerline upstream of the bifurcation and flow perturbations caused by cell obstruction in the bifurcation region. Cell migration, which arises because of flexibility, causes more nonuniform partitioning while cell obstruction causes more uniform partitioning. Bifurcations with differently sized daughter vessels experience, on average, a higher red blood cell flux into the smaller branch. Partitioning is unaffected by daughter branching angles.The motion of two interacting cells is also considered. In diverging bifurcations several types of interactions were found, in which the presence of a nearby cell causes a cell to enter a different branch than it would have otherwise. The net effect of these interactions is to cause more uniform partitioning. In wall-bounded linear shear flow, a two-dimensional swapping interaction was identified, in which two cells on different background fluid streamlines approach each other, slowly move onto their partner's streamline, and then move away from each other.The simulations produced by this two-dimensional model provide insight into the effects of red blood cell deformability, bifurcation geometry and volume fraction of red blood cells on red blood cell partitioning and on the resultant distribution and transport of materials in the microvasculature.