A mesoscale computational model is developed for efficient simulation of transport, collision, and adhesion of blood cells, which can be applied to red blood cells (RBCs), white blood cells (WBCs), and platelets in three-dimensional (3D) blood flow where the fluid length scale is substantially larger than the particle length scale. Physically justifiable approximations are introduced to accommodate computations with large numbers of cells, O(10 ⁴-10⁵). For instance, cells are modeled as elastic particles, and non-spherical RBC and platelet shapes are approximated as ellipsoidal. Fast identification of particle collision is accomplished by a novel method based on particle level-surfaces. Rapid computational speed is also achieved by utilizing a model of receptor-ligand binding to approximate cell adhesion. Under certain further approximations, it is demonstrated that receptor-ligand binding can be cast in a form mathematically analogous to van der Waals adhesion with time-varying adhesive surface energy density. Further acceleration results from use of a multiple-time-step algorithm. A level-set field method is incorporated into the model for representation of complex geometries. Novel measures of aggregation of particles are developed and utilized to study the size and structure of aggregates. The computational model yields expected results and compares favorably with experimental and theoretical data for RBC aggregate size, margination of WBCs and platelets due to RBC aggregation, and effective blood viscosity. Two-dimensional (2D) simulations are shown to be valid in that ellipses fit to planar projections of aggregates have the same shape and size as in 3D simulations of channel flows. For shear flows with large adhesion energy, 2D aggregates are more elongated into chain-like structures than the more ball-like aggregates in 3D. In bifurcation flows, the computational model performs well in simulating plasma skimming, compared to experimental and computational studies. Collision of particles with each other in bifurcating flows is discovered not to affect which branch a particle enters, but to affect some particle trajectories and the amount of collisions between particles and walls after the bifurcation point.