A novel numerical simulation of adhesive particles (cells) reversibly interacting with an adhesive surface under flow is presented. Particle--particle and particle--wall hydrodynamic interactions in low Reynolds number Couette flow are calculated using a boundary element method that solves an integral representation of the Stokes equation. Molecular bonds between surfaces are modeled as linear springs and stochastically formed and broken according to postulated descriptions of force-dependent kinetics. The resulting simulation, Multiparticle Adhesive Dynamics, is applied to the problem of selectin-mediated rolling of hard spheres coated with leukocyte adhesion molecules (cell-free system). Simulation results are compared to flow chamber experiments performed with carbohydrate-coated spherical beads rolling on P-selectin. Good agreement is found between theory and experiment, with the main observation being a decrease in rolling velocity with increasing concentration of rolling cells or increasing proximity between rolling cells. Pause times are found to increase and deviation motion is found to decrease as pairs of rolling cells become closer together or align with the flow.