A numerical model of transient diffusive mass transfer through a circular hole that connects two semiinfinite media was used as a means of determining potential effects of waste container penetrations on the release of immobilized contaminants into the environment. The finite difference model as developed necessarily includes treatment of mass transport in both the waste and surrounding medium and allows calculation of release rates for cases with and without preferential adsorption and differing diffusivities of the two media. The dimensionless contaminant release rate was found to vary over several orders of magnitude depending on the product of the ratio of the distribution coefficient and the media diffusivities only. As would be intuitively expected, partitioning favoring the surrounding medium and higher relative waste medium diffusivity cause higher transport rates. There was definitely no unexpected enhancement in the release rate in the case of perforations over that of an uncontained waste form.