The heterogeneous nature of the pore space of rocks was numerically simulated by varying the proportions of empty and filled bonds and nodes on a square lattice. A filled bond could contain a tube or a crack or both, the dimensions of which were randomly chosen. For each of 100 network realizations, the permeability, k, electrical formation factor, F, connected porosity, &PHgr;, specific surface area, A, and their pressure dependences were calculated. This large simulated database was then used for testing the validity of several models from the literature. The main result of this work is that permeability was well predicted by the relation k=R2/(8F), where R is an appropriate length scale. This relation was better satisfied by using the Katz-Thompson (KT) critical radius for R rather than the Schwartz-Sen-Johnson (SSJ) hydraulic radius. In particular, the SSJ model was found to be more sensitive to the pore shape heterogeneity than was the KT model. It yielded estimates of k of equal (if not better) quality than did the KT model when only one type of channel was considered (cracks or tubes), but more scattered results were obtained when it was applied to mixtures of cracks and tubes. ¿ American Geophysical Union 1995