Summary This paper describes the behavior of a naturally fractured reservoir when a well is producing through a vertical fracture with uniform flux or infinite conductivity. The reservoir model is a double-porosity medium, and both pseudo-steady-state and transient-interporosity-flow models are studied. The derivative vs. time for each solution is shown, and an analysis method for matching field data to such a model is presented. This study combines a reservoir and a well model, both of which have been extensively studied separately. Included are a quick review of the main characteristics of these models and the methods used to solve the problems. At the end of the study, a general method is suggested to extend models with constant boundary conditions—e.g., homogeneous and double-porosity cases.