Hexavalent uranium (U(VI)) can be immobilized by various microbes. The role of extracellular polymeric substances (EPS) in U(VI) immobilization has not been quantified. This work provides a model framework to quantify the contributions of three processes involved in EPS-mediated U(VI) immobilization: adsorption, bioreduction and desorption. Loosely associated EPS was extracted from a pure bacterial strain, Klebsiella sp. J1, and then exposed to H₂ and O₂ (no bioreduction control) to immobilize U(VI) in batch experiments. U(VI) immobilization was faster when exposed to H₂ than O₂ and stabilized at 94% for H₂ and 85% for O₂, respectively. The non-equilibrium data from the H₂ experiments were best simulated by a kinetic model consisting of pseudo-second-order adsorption (k_a = 2.87 × 10⁻³ g EPS·(mg U)⁻¹·min⁻¹), first-order bioreduction (k_b = 0.112 min⁻¹) and first-order desorption (k_d = 7.00 × 10⁻³ min⁻¹) and fitted the experimental data with R² of 0.999. While adsorption was dominant in the first minute of the experiments with H₂, bioreduction was dominant from the second minute to the 50^th min. After 50 min, adsorption was negligible, and bioreduction was balanced by desorption. This work also provides the first set of equilibrium data for U(VI) adsorption by EPS alone. The equilibrium experiments with O₂ were well simulated by both the Langmuir isotherm and the Freundlich isotherm, suggesting multiple mechanisms involved in the interactions between U(VI) and EPS. The thermodynamic study indicated that the adsorption of U(VI) onto EPS was endothermic, spontaneous and favorable at higher temperatures.