A technique has been developed to measure the linear mass density of fibers and ribbons, and adapted to the study of stress/strain coupled diffusion in polymeric materials. The technique overcomes the limitations of sensitivity and range, typical of traditional diffusion measurement techniques, and can be used for a wide range of fiber densities. It is also possible to monitor stress or strain within the fiber while measuring the change in mass, without requiring the fiber to be at equilibrium or interrupting the experiment. Estimates of material property changes, as exemplified by tensile modulus changes, can also be made during the course of the experiment. The mass per unit length, at any given time, of polymer fibers or ribbons under known stresses and strains can be determined by this technique. From this it is possible to estimate the gain or loss in weight in the sample due to permeants diffusion. Some preliminary result of constant strain and constant stress experiments on ribbons of polycarbonate, polyimide, and precured epoxy, and KevlarR monofilaments, are discussed and the scope and resolution of the apparatus are indicated.