Heavy oil is the most important resource to supplement the loss of oil in the 21st century. The International Energy Agency (IEA) estimates that there are 6 trillion barrels of heavy oil worldwide. Currently, the standard heavy oil production is based on steam injection, which faces a great challenge because of the sand production, gas channelling, and high costs. Cold Heavy Oil Production with Sand (CHOPS) has extremely good primary performance, high oil production rates, high primary recovery factors, and low operational costs. In this paper, the mathematical and numerical descriptions are given for the sand production within the context of continuum mechanics and finite dements, with emphasis on the physics of the sand production and its relation to the interaction between hydrodynamics and geomechanics. A mathematical model is proposed based on the erosion mechanics, while the instability associated with the sand production is treated within the framework of the high gradient continuum mixture theory. Numerical results of the proposed model are in good agreement with the oil field data, which shows that the model could be applied to predict the oil production and to provide a guidance to adjust the explore strategy. Moreover, the influencing factors, such as oil viscosity, producing pressure drop and information coefficient on CHOPS performances are discussed, which helps to determine what kind of reservoir is relevant for the application of the CHOPS. At last, the advantages and disadvantages of the model are discussed in detail and the future work of modeling cold production is commented.