A complete understanding of fluid exchanges in tissues and organs requires knowledge of the permeability of their delimiting membranes as a function of the finite strain that they experience. One reason for the current dearth of data in the literature is the need for new theoretically motivated experimental approaches. In this paper, we use a general scaling to identify non-dimensional parameters that are measured easily by combining a simple pressure-driven diffusion chamber with a method to induce equibiaxial and homogeneous finite strains that can be measured via a non-contacting video system. Illustrative results on excised bovine epicardium reveal a nonlinear relationship between a non-dimensional permeability and finite strain up to stretches of 60%.