The dynamics of transport processes, such as hydrogen transport in metals, can only be obtained from non-steady-state techniques. We have derived the relevant expressions for the phase shift and magnitude of the transfer function describing the response to a modulated flux at one surface of a foil. The expressions include the influence of trapping and surface effects. Experimental measurements of the phase shift and magnitude on annealed palladium foils agree with the model taking D = 3 x 10(-7) cm(2) s(-1) and no trapping or surface effects. Experiments on palladium foils with poor surface treatment exhibited an increase in the phase shift and decrease in the magnitude across the accessible frequency range, consistent with surface effects. These results demonstrate that modulation permeation spectroscopy can be used to study transport in metallic foils.