Abstract It is expected for naturally occurring formations that the transition period of flow from fissures to matrix takes place during the radial flow regime. However, depending upon the value of the interporosity flow parameter, this transition period can show up before or after the radial flow regime. First, in a heterogeneous formation which has been subjected to a hydraulic fracturing treatment the transition period can interrupt either the bilinear or linear flow regime. Once the fluid inside the hydraulic fracture has been depleted, the natural fracture network will provide the necessary flux to the hydraulic fracture. Second, in an elongated formation, for interporosity flow parameters approximated lower than 1×10-6, the transition period takes place during the formation linear flow period. It is desirable not only to appropriately identify these types of systems but also to complement the conventional analysis with the adequate expressions to characterize such formations for a more comprehensive reservoir/well management. So far, the conventional methodology does not account for the equations for interpretation of pressure tests under the above two mentioned conditions. Currently, an interpretation study can only be achieved by non-linear regression analysis (simulation) which is obviously related to non-unique solutions especially when estimating reservoir limits and the naturally fractured parameters. Therefore, in this paper, we provide and verify the necessary mathematical expressions for interpretation of a vertical well test in both a hydraulically-fractured naturally fractured formation or an elongated closed heterogeneous reservoir. The equations presented in this paper could provide good initial guesses for the parameters to be used in a general nonlinear regression analysis procedure so that the non-uniqueness problem associated with nonlinear regression may be improved.