Abstract: In order to solve the problem of sand production in gas-wells of perforated completion, a three-dimensional model for sand production of elastic-plastic gas formation is established based on the law of effective strain, and is then solved by the nonlinear finite element method. The trend of stress and effective plastic strain distribution in the near wellbore area is investigated according to the computation results, and it is found that the maximum effective strain occurs at the top and bottom of the starting position of perforations, where sand production is prone to happen. The critical bottom hole pressure decreases with the increasing of formation pressure, weakening the trend of sand production. The critical bottom hole pressure depends on the rock properties, fluid characteristics, values of geo-stresses and formation pressure comprehensively, and sand produced can be reduced under stable and high formation pressure and by following consistent production procedures. The model can be used under general conditions of practical geo-stresses, complex geometry and perforation proposal, and variable rock and gas properties.