Abstract: In recent decades, the earth fissure induced by groundwater withdrawal has been studied around the world and many remarkable achievements have been obtained. Generally speaking, there is no unified conclusion about the mechanism of the earth fissures’ formation. In research on numerical simulation of earth fissure, the models have experienced the development from one-dimensional to multiply-dimensional, from uncoupling to Fluid-Solid Coupling, from elastic to elastic-plastic and visco-elastic-plastic, from qualitative to semi-quantitative. Since the complexity of earth fissure formation, current research is far from mature, thus many problems remain unsolved.