Influence of self stress on the transport of a guest in a host matrix is studied within the process of hydrogen permeation through a large thin membrane having properties similar to those of palladium or Pd81Pt19 alloy. The equilibrium in the system is perturbed at one side of the membrane by a sinusoidal signal of hydrogen concentration. At the opposite side, the hydrogen concentration is maintained at its initial value, and the flux of hydrogen is the response. The transport equations are solved numerically for a wide range of frequencies and amplitudes of the perturbing signal. At the periodic steady state, the larger the signal amplitude, the more important become the zero and higher harmonics of the flux, accompanying the fundamental harmonics. The presence of the zero harmonics causes a permanent pumping of hydrogen throughout the membrane. The fundamental harmonics closely reproduces the results obtained by solving the linearized transport equations. This means that, up to the largest amplitudes, the frequency spectrum of the fundamental harmonics allows for obtaining reliable values of the diffusion coefficient of hydrogen and the bulk elastic modulus of the metal matrix.