Microspheres (referred commonly as beads) are being extensively used in biochemical assays as supports for proteins, DNA, etc. We have successfully developed computational models for simulating sample detection using flowing beads. The model fully integrates Lagrangian transport of the beads, convective-diffusive transport of analyte and biomolecular binding reactions on the bead surfaces. The Eulerian-Lagrangian transport equations that govern the entire process are presented. Model inputs are the geometry, bead and sample transport properties, and surface binding kinetics along with assay protocol such as flow rates etc. with surface coverages on the beads as output. Quantitative capabilities of the model are demonstrated using an immunoassay [IL-2 binding with IL- 2Ra] in a typical Y-junction.