Lateral flow (LF) bio-detectors facilitate low-cost, rapid identification of various analytes at the point of care. The LF cell consists of a porous membrane containing immobilized ligands at various locations. Through the action of capillary forces, samples and reporter particles are transported to the ligand sites. The LF membrane is then scanned or probed, and the concentration of reporter particles is measured. A mathematical model for sandwich assays is constructed and used to study the performance of the LF device under various operating conditions. The model provides insights into certain experimental observations including the reduction in the level of the detected signal at high target analyte concentrations. Furthermore, the model can be used to test rapidly and inexpensively various operating conditions, assist in the device's design, and optimize the performance of the LF device.