Abstract: Carbon dioxide geological storage technology is an effective way to reduce carbon dioxide emissions. The sandstone lens is an ideal site for carbon dioxide storage because of its good combination of reservoir cover. During the supercritical carbon dioxide injected into sandstone lens, a series of complex problems including fracture initiation, extension and evolution directly determine the safety of storage. The numerical simulation software ABAQUS that is based on the extended finite element method(XFEM) is used in this study. The study uses the changes of the main keywords to set up fluid-solid coupling model. Then the process of injecting supercritical carbon dioxide into sandstone lens is observed to find out the fracture failure process in the internal sandstone lens reservoir. Several conclusions are drawn from the simulation as follows. Under the condition of different lens shapes, the velocity of the inclined lens is faster than that of the horizontal lens, and the pore pressure at fracture initiation is much larger. The propagation time is short, and the CO₂ storage ability is poor. As three different kinds of CO₂ injection flowing rates increase, the pressure increase is more obvious, the initiating cracking time is shorter, the fracture propagation time is shorter and the speed of propagation is faster. However, the length and shape of the fracture do not change significantly. In the process of the fracture propagation, the fracture widens firstly and becomes the diversion channel, and then grows. The stress at the fracture tip increases first and then decreases gradually. The fracture stops expanding at last.