The motion of a rigid particle suspended in a two-dimensional flow through a bifurcating channel is calculated numerically. The calculated particle trajectories depend on the partitioning of total volume at the bifurcation, the size of the particle relative to channel dimensions, and the upstream lateral position of the particle. Results are used to deduce the flux of particles in a dilute suspension entering each branch of a bifurcation as a function of the total volumetric flow entering each branch. The calculated results exhibit several qualitative features observed in experimental data for red cell flux at capillary bifurcations.