The theory of pure-Fickian diffusion of solutes through polymers is developed and explained in detail. Unique methods are presented that may be used to predict rapidly and without extensive mathematical manipulation the time in which a hydrophobic organic chemical would penetrate plastic water pipes under pure-Fickian conditions. It is demonstrated that the results are dependent on the initial boundary conditions assumed, the difference between the external and internal activity of the permeating substance, the equilibrium partitioning of the solute between the pipe wall and the water held inside the pipe, the diffusivity of the solute in the plastic, and the pipe dimensions. Limitations to the theory are discussed in detail and example solutions are presented for four groups of organic chemicals, which are then compared qualitatively with a pipe permeation incident. Includes 21 references, tables, figures.