Modeling of matrix-fracture transfer function is important in the simulation of fluid flow in fractured porous media using a dual-porosity concept. One of the main focuses of this book is to find the transfer function for the single-phase flow of compressible fluids in fractured media using the solution of nonlinear gas diffusivity equation. The developed shape factor and transfer function can be used as an input for modeling flow of compressible fluids in dual-porosity systems. Another major purpose of this study is to investigate the effect of the fracture pressure depletion regime on the shape factor and transfer function for single-phase flow of a compressible fluid. For accurate prediction of fluid transfer between the matrix and fracture systems the effect of variable block size distribution should be considered. The proposed model is also able to simulate fluid exchange between matrix and fracture for continuous or discrete block size distributions. This solution can be simplified to model flow of slightly compressible fluids like water or oil in dual-porosity (fractured porous) media.