An idealized model has been developed for the purpose of studying the characteristic behavior of a permeable medium which contains regions which contribute significantly to the pore volume of the system hut contribute negligibly to the flow capacity; e.g., a naturally fractured or vugular reservoir. Unsteady-state flow in this model reservoir has been investigated analytically. The pressure build-up performance has been examined in some detail; and, a technique for analyzing the build-up data to evaluate the desired parameters has been suggested. The use of this approach in the interpretation of field data has been discussed. As a result of this study, the following general conclusions can be drawn: 1. Two parameters are sufficient to characterize the deviation of the behavior of a medium with “double porosity” from that of a homogeneously porous medium. 2. These parameters can be evaluated by the proper analysis of pressure build-up data obtained from adequately designed tests. 3. Since the build-up curve associated with this type of porous system is similar to that obtained from a stratified reservoir, an unambiguous interpretation is not possible without additional information. 4. Differencing methods which utilize pressure data from the final stages of a build-up test should be used with extreme caution.