A model for pore pressure-dependent cleat permeability is presented for gas-desorbing, linear elastic coalbeds under uniaxial strain conditions experienced in producing reservoirs. In the model, changes in the cleat permeability of coalbeds, which are idealised to have a bundled matchstick geometry, is controlled by the prevailing effective horizontal stresses normal to the cleats. Variations in the effective horizontal stresses under uniaxial strain conditions are expressed as a function of pore pressure reduction during drawdown, which includes a cleat compression term and a matrix shrinkage term that have competing effects on cleat permeability. A comprehensive analysis has revealed that the shape of the stress - pore pressure curve is predominantly determined by the magnitude of recovery pressure and rebound pressure relative to the initial reservoir pressure. A total of five possible scenarios have been identified with regard to response of the horizontal stress function to reservoir drawdown. When applied to four coalbed wells at two separate sites in the fairway of the San Juan basin, the model predictions at one site, where the three wells have shown increased absolute permeability during gas production, are in excellent agreement with the published pore pressure dependent permeability changes that were obtained independently from history matching the field production data. At a separate site the model correctly predicts, at least qualitatively, a strong permeability rebound at lower drawdown pressures that has been inferred through history matching the production data. An analysis of the effects of initial reservoir pressure on the response of effective horizontal stress to drawdown was carried out, with reference to the range of pressure likely to be encountered in the San Juan basin. The implications of this in terms of pore pressure dependent permeability are discussed.