The effects of stresses and strains, occurring in a reservoir, on the cumulative gas production and the petrophysical properties are studied. Existing strain and stress model equations have been used to analyse the coupled effect of matrix shrinkage and cleat compressibility change on reservoir properties. A coal bed methane (CBM) gas reservoir, low permeable and undersaturated, is semi-analytically modelled. A nearly suitable model from among them is eventually proposed to predict the cleat permeability and gas production existing in the field using a dynamic drainage area (DDA) approach. These results vary with the production time. The strain model predicts gas production values and the stress models predict a range of cleat permeability variation values close to field values. Cleat permeability and cleat porosity both affect gas productivity but in the opposite manner. © 2020 Inderscience Enterprises Ltd.