The literature reveals no equation that expresses the influence of the diffusional boundary layer on diffusion-controlled sorption of dyes or other material by polymeric substrates from finite baths. In view of this mathematical void, a technique is proposed that approximates dimensionless sorption time as a function of fractional equilibrium uptake of diffusant by polymer, dimensionless dye bath exhaustion, and dimensionless boundary layer. The computational technique is based on relationships found in transitional kinetics and is shown to be applicable for sorption systems involving polymeric material of different geometrical shapes. To illustrate the technique, dimensionless half-times of sorption are computed for the case of diffusant uptake by a cylinder.