In order to study the fluid flow mechanism for cold heavy oil production with sand (CHOPS) and predict their production performance precisely, criteria for the skeleton sand erosion and movable sand startup have been set up, based on the stress analysis on formation rock and sand particulates. According to the principles of effective stress, mass conservation, virtual displacement, equivalent virtual work and so on, both the single-well-black-oil model of CHOPS with three dimensions and four phases and the equilibrium equation of borehole wall rock with elasto-plastic deformation have been established. Considering the basic definitions of physical property parameters and the effect on physical property parameters caused by bulk strain, skeleton sand erosion, movable sand deposition on the pore surfaces and movable sand bridge plug at pore throats, dynamic models of physical property parameters have been established for numerical simulation of CHOPS. Then, the coupling solutions of the model have been studied. Finally, a case to verify the correctness and validity of the model is simulated and analyzed. The establishment of the mathematic model describing the fluid flow mechanism of CHOPS is of great significance to help us recognize correctly and exploit heavy oil reservoirs efficiently.