The effects of self-stress on the concentration transfer function of hydrogen diffusion in a continuous elastic solid-metal matrix were analyzed. A large thin-plate metal specimen saturated with hydrogen is the essential part of the system. The equilibrium is perturbed by a small-magnitude sine-wave input signal of hydrogen concentration applied at one surface of the specimen. In response, oscillations of hydrogen concentration appear at the opposite surface. The concentration transfer function is defined as the ratio of the stationary response to input signals. The derived diffusion equations are non-linear. They are linearized, and then solved analytically. The resulting transfer function is discussed in terms of hydrogen permeation through a specimen of properties similar to palladium and Pd81Pt19 alloy, in wide ranges of hydrogen concentrations in the metal matrix and of frequencies of the signal. At relatively high frequencies, the system is highly sensitive to non-Fickian diffusion, resulting from the non-local effect of self-stress. Transfer function spectroscopy seems to be a more powerful tool for studying the hydrogen transport in self-stressed metals than the commonly used transient break-through method. In particular, it should allow the dependence of the hydrogen diffusion coefficient and of the elastic modulus of metal-hydrogen solids on the hydrogen concentration to be studied.