Leukocyte rolling and arrest on the vascular endothelium is a central event in normal and pathological immune responses. However, rigorous estimation of the fluid and surface forces involved in leukocyte-endothelial interactions has been difficult due to the particulate, non-Newtonian nature of blood. Here we present a Lattice-Boltzmann approach to quantify forces exerted on rolling leukocytes by red blood cells in a "virtual blood vessel." We report that the normal force imparted by erythrocytes is sufficient to increase leukocyte binding and that increases in tangential force and torque can promote rolling of previously adherent leukocytes. By simulating changes in hematocrit we show that a close "envelopment" of the leukocyte by the red blood cells is necessary to produce significant changes in the forces. This novel approach can be applied to a large number of biological and industrial problems involving the complex flow of particulate suspensions.