endothelial or epithelial tissues form semipermeable barriers that restrict and regulate the transport of solutes to their surrounding tissues. Microphysiological systems aim to recapitulate this hallmark function and provide models for e.g. drug screening. Here, we develop, and validate by extensive simulations, two assays dedicated to the characterization of diffusion- and pressure-driven transport across epithelial and endothelial ductal tissues fabricated in collagen matrices. We first prove that, upon pressure actuation, barrier crossing is enhanced, although transport in paracellular space remains dominated by diffusion. Using the monopore model, we show that diffusion-driven measurements are consistent with paracellular pore radii of 2.1 and 24 nm for epithelial and endothelial tissues, respectively, but also demonstrate that these estimates fail to account for pressure-driven transport data. We solve this contradiction by introducing the deformable monopore model, which assumes the same pore sizes of 2.1 and 24 nm, and includes the deformation, essentially elongational thinning of paracellular cleft, induced by intraluminal stress to fit pressure-driven transport. Hence, this study suggests that transport through barrier tissues can be regulated by mechanical strain