An elasto-plastic, fully-coupled fluid flow and deformation finite element model is proposed for modelling development of both shear and tensile failure; the latter representing the volume of the solids that are in a liquefied state and hence ready to be transported and produced. The model takes account of the changes in permeability in accordance with changes in the stress state (or porosity), including failure. This feature allows for computation of the changes in skin as the reservoir is depleted and sand is produced. One of the key aspects of the model is its employment of the modified Mohr-Coulomb failure envelope along with several numerical algorithms to effectively simulate shear and tensile failure in a numerically accurate and stable form. The modified failure envelope provides a means of capturing the strong non-linearity in the failure envelope for the weak rock formation around the wellbore before solids production. In that state, the material is practically in a disaggregated state due to shearing, yet it has a high density. The most important feature of this model is its capability to capture the episodic nature of drawdown induced sand production. Verification and application of this model to a well-documented openhole cavity completion in coalbed methane in the San Juan Basin is shown in a companion paper.