This paper presents a multiscale model developed for the modelling of multiphase flow in fractured reservoirs, particularly in coal seams during coalbed methane recovery (or carbon dioxide storage). The variation of gas content in the matrix induces a shrinkage/swelling of the material which is likely to affect the fractures and thus the permeability of the rock. In addition, the permeability is also sensitive to the effective stress evolution. In order to simulate the reservoir production taking into account the cleat-scale phenomena on their specific length, a cleat-scale model is used for the modelling of the Representative Elementary Volume (REV at microscale). This cleat-scale model is integrated in a multiscale approach using the finite element square method. It consists to localize the macroscale deformation to the microscale by applying appropriate boundaries, then resolve the boundary value problem on the microscale with finite elements, then homogenize the microscale stresses with appropriate averages to compute macroscopic quantities, and finally resolve the boundary value problem on the macroscale with finite elements. This approach has the advantage that it does not require to write some constitutive laws at the macroscale but only at the REV-scale. The model is developed and implemented in a finite element code and then used for reservoir modelling. A synthetic case is first considered to demonstrate the ability of the model to obtain some bell-shape production curves as expected for unconventional reservoirs. Finally, a history matching exercise is carried out.