The transport of radionuclides through penetrations in wastes containers is analyzed. Penetrations may result from corrosion or cracks and may occur in the original container material, in degraded or corroded material, or in deposits of corrosion products. In this report we do not consider how these penetrations occur or the characteristics of expected penetrations in waste containers. We are concerned here only with the analytical formulation and solutions of equations to predict rates of mass transfer through penetrations of specified size and geometry. Expressions for the diffusive mass transfer rates through apertures are presented in Chapter 2, and numerical illustrations are presented in Chapter 3. The calculations show that mass transfer through small penetrations in thin-wall containers can be great enough that the penetrated container is no longer an effective barrier for radionuclide release. Use of this theory to calculate mass transfer through thick-wall containers is the subject of a later report. 3 refs., 9 figs.