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The one-dimensional transport of radionuclides and their decay products from an underground nuclear waste isolation site through the surrounding geologic media to a surface environment is modeled. An ambiguity in the application of the previously reported mathematical solution for this problem has been clarified. The results of applying the solution described here compare favorably with the results of applying the former solution, but the present solution is computationally more efficient and less subject to numerical errors. Thus, this solution is presently being used by the authors and others to evaluate the sensitivity of potential radioactivity releases into the environment to the characteristics of various nuclear waste isolation systems. The model is expected to be used in the future as an analytical standard to which the accuracy of numerical codes can be compared.