The ability to develop predictive mathematical models of therapeutic release from pharmaceutical formulations has enormous potential to enhance our understanding of such systems and improve the controlled release of the payload. The current work describes the development and testing of a one-dimensional model of drug transport from amorphous, swelling/dissolving polymers. Model parameters such as the diffusivities of water and drug, the initial loading of the drug, the polymer dissolution rate, drug-polymer interactions, and the tablet thickness were varied, demonstrating the ability to tune the release to be controlled by either drug diffusion or polymer chain disentanglement. In addition, predictions of the concentration profiles of water and drug within the gel layer, the locations of the erosion and swelling boundaries, and gel layer thickness were obtained for diffusion- and disentanglement-controlled release. To highlight the generalizability of this model, multiple parameters were varied, and it was shown that increasing the diffusivities of water and drug and the initial drug loading and decreasing the polymer dissolution rate sufficiently resulted in diffusion-controlled release. The model was fit to experimental data for a model tablet system comprising of sodium diclofenac entrapped in a poly(vinyl pyrrolidone) matrix and yielded physically meaningful values of the model parameters. The work presented here demonstrates the predictive power of the model for rapid and rational design of future pharmaceutical formulations for controlled drug delivery.