The microgeometry or texture of a porous medium determines its physical properties, e.g., the electromagnetic, acoustical, and fluid dynamic properties of sedimentary rock. Unified functional models of texture are clearly needed to test and provide insight for texture‐dependent theories relating different properties or explaining empirical observations. A class topological models of sedimentary rock is introduced, together with the necessary topological concepts. Each sample is modeled by two 3‐D networks, pore and grain, together with a set of measured parameters such as integranular contact areas or pore/throat ratios (of which any given application may use only a subset). An intuitive example of thin modeling process is provided. A description is given of data acquisition and image analysis procedures used for measurements from reconstructed serial rock sections. Preliminary observations of grain and pore statistics are presented, with comparisons to other related data. The ’’connectivity’’ of the pore (or grain) system of Berea is lower than the connectivities of regular monosized sphere packs with similar porosities and the same mean grain ’’diameters’’. A wide distribution of sizes, aspect ratios, and coordination number were also found for Berea. Illustrative applications of this kind of modeling to nuclear‐magnetic resonance, fluid flow, and frame modulus are given.