This work presents a new approach to the investigation of mass transport processes in polymers. The coefficient of water diffusion in polyacrilonitrile was measured using fiber optic evanescent wave spectroscopy (FEWS). Unclad AgCIBr fibers of 0.9 mm diameter were dipcoated by PAN layers of 1-10 μm thickness. The transmission of the fibers in the mid-IR was measured using a Fourier transform infrared (FTIR) spectrometer. The penetration of water into these layers gave rise to significant changes in the measured spectrum. These changes were used for diffusion studies in situ. The novel statistical approach to the analysis of spectra was developed for the purpose of calculating the diffusion coefficient, D, using spectral data. This analysis reveals the specific wavelengths which have been taken into account for the calculation of D. The FEWS procedure, combined with statistical treatment of the spectral data, offers a high accuracy in the calculation of parameters of diffusion. It must be emphasized that the cylindrical symmetry of our fibers renders them especially suitable for the diffusion study and allows us to obviate the difficulties caused by end effects.