Diffusion-controlled, isothermal sorption (or desorption) of diffusants by cylindrical polymeric materials can be modeled for finite bath conditions by the use of the conventional diffusion equation solutions of Wilson or Crank when certain limiting assumptions apply. Iterative determination of diffusion coefficients by the use of these advanced equations, however, requires accurate "seed roots" for efficient solution. An empirical seed root generating function has been found that is so very accurate that it can be used in place of the conventional diffusion equation solutions for all but the most extreme levels of definitude. The parameters of the empirical equation as functions of equilibrium bath exhaustion are given, and values of fractional equilibrium uptake, M(t)/M(infinity), as a function of dimensionless time, Dt/r(2), found by the use of both the diffusion equation solutions and the empirical equation are compared.