An elastic-plastic three-dimensional fully coupled model is proposed to model shear and tensile-induced sanding and consequently estimate volume of sand production. The problem is of significant interest to industry since a good estimation of wellface failure and therefore sand production helps the completion engineer to best design downhole completions. Such a design would not only maximize flow rate but also minimize cost of completion. In this investigation, a numerical analysis by using the finite difference method was performed. An elastic-plastic analysis by using the Mohr-Coulomb model was conducted. This model is indeed considered to be the most useful model for geotechnical analysis. For the purpose of this study, the openhole case was considered to have had large deformation and large plastic strains in order to determine the wellface failure and therefore sand production. Effective stress distributions around a wellbore were investigated. Based on this investigation, an effective way to model depletion-induced sanding is proposed. The effects of cohesion, friction angle, and modulus of elasticity as well as reservoir pressure on the critical bottom hole pressure were examined. The results show that the cohesion and the variation in friction angle affect the critical value of drawdown, the effect of the former one being more significant than the latter. Moreover, the modulus of elasticity and reservoir pressure affect the critical value of drawdown significantly. At higher values of the modulus of elasticity, however, the effect of the modulus of elasticity tapers off and a further increase in its value does not affect the critical value proportionally. The effect of the reservoir pressure on acceptable drawdown value indicates the effect of reservoir depletion on the potential of sand production.