The present paper addresses the leaching of hazardous contaminants from immersed and replenished materials and from granular materials flushed in a column. First, the leaching of an immersed material in contact with a limited volume of leachant is studied. The mass transfer from material to leachant is assumed to be inversely proportional to vt (i.e. following the semiinfinite medium diffusion model). The leaching model accounts for the concentration of the contaminant in the leachant, the (deviation from) equilibrium partition of the contaminant between material and leachant, and leachant replenishment. The governing equations are solved in closed form, yielding the contaminant concentration in leachant and monolith versus the elapsed time. For special cases this solution corresponds to the leaching expressions obtained by Godbee and Joy (1974). Subsequently, the unsteady leaching process from a granular material packed in a column, flushed by a leachant, is modeled. Here, the mass transfer from material to leachant is also assumed as inversely proportional to vt. The model leads to a moving boundary problem, the governing partial differential equations are transformed and solved using asymptotic techniques. Approximate expressions are obtained for the contaminant concentration of the material and in the leachant. Of special practical interest is the leachant concentration at the exit of the column as here the leachant can be collected in flasks and analyzed. Finally, the models are generalized to systems where the mass transfer is an arbitrary power function of time. The resulting equations can for instance be used for determining an effective diffusion coefficient and/or comparing immobilization yields.