Quantitative understanding of kinetics and mechanisms heavy metal adsorption-desorption and transport processes, batch and stirred-flow experiments were carried out with vanadium (V) and molybdenum (Mo) on soils at different reaction conditions and time scale. Batch experiments indicated that adsorption of V and Mo on soils were highly nonlinear and time-dependent, where V and Mo retention showed typical biphasic reaction kinetics. The stirred-flow experiments showed that both V and Mo adsorption consisted of a fast initial reaction, as indicated by the fact that effluent solute concentration was close to zero for the first few minutes. A stirred-flow multi-reaction model (MRM) which accounts for slow as well as fast reactions of the reversible and irreversible type was developed to describe V and Mo adsorption and desorption processes on soils. Based on model simulations and experimental tracer breakthrough curves (BTCs) results, we concluded that the proposed model is valid for stirred-flow conditions. The strong retardation and slow release behaviors of V and Mo from stirred-flow experiments were successfully described using the proposed stirred-flow MRM where retardation and irreversible reactions were necessary. Our work provide a general stirred-flow model which is capable of describing reactive and non-reactive solutes.