The diffusion equation of low molecular weight substances (penetrant) into a coaxial cylinder of multiple components (m) was formulated in general and solved rigorously. As the simplest but a practical case of m = 2, which corresponds to the diffusion of penetrant into fibrous material with skin and core structure, the diffusion of penetrant was analyzed in detail. That is, changes in the penetrant concentration distribution within the coaxial dual cylinder of skin and core components and the total amount of penetrant sorbed within the cylinder both with time after exposing the cylinder to atmosphere of fixed penetrant concentration of C(out) were calculated with variation of the diffusion coefficient ratio (D1/D2) and the radius ratio (R2/R1), where D1 and D2 are the diffusion coefficients of penetrant in the core and the skin, and R2 and R1 are the radii of the fibrous material and the core, respectively. Keeping (R2/R1) at a constant value of 1.2 but varying (D1/D2) from 10(4) to 10(-2), the penetrant concentration distribution was calculated and found to be much different particularly within the core between (D1/D2) > 1 and (D1/D2) < 1. The sorption curves were also found to deviate in their respective ways from that of Fickian curve of a homogeneous cylinder with (D1/D2)= 1 except at initial stage of sorption. Further, by keeping (D1/D2) constant but varying (R2/R1) from 1.1 to 1.5, the effects of relative skin thickness upon the sorption curve were studied.