Lateral flow (LF) biodetectors facilitate low-cost, rapid identification of various analytes. The LF cell consists of a porous membrane containing immobilized ligands at various locations. Through the action of capillary forces, a mixture of sample and reporter particles is transported to the ligand sites, where the target analytes and the reporters bind to the immobilized ligand. The concentration of the reporters is measured with a scanner. A mathematical model for two different competitive assays is constructed and used to study the performance of LF devices under various operating conditions. The model predicts the signal magnitude as a function of target analyte, reporter, and ligand concentrations, reaction rate constants, and flow rate. The predictions are compared and qualitatively agree with experimental data. The model provides insights into various experimental observations. Furthermore, the model can be used to optimize the performance of LF devices and to inexpensively and rapidly test the system under various operating conditions.