Due to the discontinuity and unknown locations, it has been still a great challenge to numerically model pumping-induced earth fissuring. A coupled quasi-static material point method was proposed in this paper to model the initiation and propagation of earth fissures. The main advantages of this method lie in that it does not need to give the locations of the earth fissures in advance and whether a fissure initiates and propagates or not is only determined by the local stress. The sensitivity analyses were also conducted in the paper to investigate the effect of individual geometric parameters on the opening and depth of fissures. Finally, the method was applied to model the pumping-induced earth fissures in Wuxi, China, where groundwater was heavily extracted in the past decades. The model results are helpful for groundwater management and earth fissure prevention.