New mathematical models are formulated and analytical solutions are presented for the diffusional release of a solute from both non-erodible and biodegradable multi-layered slab matrices in which the initial drug loading c0 is greater than the solubility limit cs. A Stefan problem with moving boundaries results from this formulation. An inward moving diffusional front separates the reservoir (unextracted region) containing the undissolved drug from the partially extracted region. The cumulative mass released is determined as a function of time. The ultimate goal of such an investigation is to provide a reliable design tool for the fabrication of specialized implantable capsule/drug combinations to deliver prespecified and reproducible dosages over a wide spectrum of conditions and required durations of therapeutic treatment. Such a mathematical/computational tool may also prove effective in the prediction of suitable dosages for other drugs of differing chemical or molecular properties without additional elaborate animal testing.