A resonant cavity method is described for the determination of the dielectric constant of polymeric solids in the form of fibers, films, and thin cylinders. Methods for investigating electrical anisotropy are outlined. In the case of fibers, for the electric field parallel to the fiber axis, the dielectric constant is determined directly. For the electric field perpendicular to the fiber axis, the problem arises of calculating the dielectric constant of the fiber from that of an air‐fiber mixture. For the latter purpose the Lichtenecker equation was found to be applicable. Illustrative measurements of the dielectric constant of wool, Nylon, and Cellophane are presented and discussed briefly.