Heavy oil is the most important resource and the way to replenish the loss of oil in the 21st century. Cold Heavy Oil Production with Sand (CHOPS) is an effective and important method to exploit heavy oil reservoir with the low cost. By describing the applicable condition and mechanism of CHOPS, the introduction of establishment about the mathematical model of CHOPS is educed; it mainly includes engineering method sand production model, continuous method of hydrodynamic model, water dynamics erosion model coupling geological mechanics, discontinuous method model, and foamy oil model. For each type of model, it gives researchers different methods to establish the mathematical model according to different factors, at the same time the models have been evaluated and compared with each other. Due to the complexity of the mechanism of CHOPS,in order to form a model which is more perfect and more close to the actual production, more influence factors should be gradually added in the future. Finally, for the application prospect and subsequent development technology of CHOPS, some own viewpoints are presented for the discussion.