A key consequence of the presence of void space within rock is their significant influence upon fluid transport properties. In this study, we measure changes in elastic wave velocities (P and S) contemporaneously with changes in permeability and porosity at elevated pressure for three rock types with widely different void space geometries: a high-porosity sandstone (Bentheim), a tight sandstone (Crab Orchard), and a microcracked granodiorite (Takidani). Laboratory data are then used with the permeability models of Guéguen and Dienes and Kozeny-Carman to investigate the characteristics that different void space geometries impart to measured permeabilities. Using the Kachanov effective medium theory, elastic wave velocities are inverted, permitting the recovery of crack density evolution with increasing effective pressure. The crack densities are then used as input to the microcrack permeability model of Guéguen and Dienes. The classic Kozeny-Carman approach of Walsh and Brace is also applied to the measured permeability data via a least squares fit in order to extract tortuosity data. We successfully predict the evolution of permeability with increasing effective pressure, as directly measured in experiments, and report the contrast between permeability changes observed in rock where microcracks or equant pores dominate the microstructure. Additionally, we show how these properties are affected by anisotropy of the rock types via the measured anisotropic fabrics in each rock. The combined experimental and modeling results illustrate the importance of understanding the details of how rock microstructure changes in response to an external stimulus in predicting the simultaneous evolution of different rock physical properties.