This paper, the first of a two-part series, provides a sound background of the volumetric response of sorptive porous media to gas depletion under in situ boundary conditions in producing reservoirs. As a first step, the overall rock matrix deformation is split into two separate components, elastic deformation caused by mechanical decompression and the nonelastic swelling or shrinkage strain induced by adsorption or desorption of gas. The shrinkage or swelling compressibility is estimated by the first derivative of pure adsorption or desorption strain with variations of gas pressure. The pore volume, or fracture, compressibility is then estimated by application of a semi-empirical model under uniaxial strain conditions. Based on the proposed model, both shrinkage or swelling and pore volume compressibilities show strong pressure dependence for sorbing gases and are thus variables for which gas production is controlled by desorption of gas. In Part 2, the experimental work under best-replicated in situ conditions is described in detail along with the results obtained and application of the theory presented in this paper.