The collapse caused by groundwater extraction in karst area is caused by the interaction between fluid and mechanic field essentially. A fluid-solid coupling model is needed to quantify the settlement and the stress around the cave. The governing equation of fluid-solid fully coupled model is derived from the continuum mechanics. Combining with the constitutive equations such as permeability and stress-strain relation, the closed mathematic description was given. The effectiveness of the model was verified by comparing with classical example, and the difference between the fully coupled model and the semi-coupling model was analyzed. Based on the engineering conditions of karst collapse area in Shenzhen, the temporal-spatial distribution was computed under the different working conditions, such as pumping rate, hole diameter and hole shape etc. The mechanical mechanism of karst collapse and subsidence was expounded. Grey correlation matrix was established based on grey theory to determine the sensitivity of each influencing factor. The results show that the coupling effect should be considered when the seepage occur in soil. The stress concentration caused by hydraulic pressure drop is the main factor of ground settlement and cave collapse. The settlement is more sensitive to the pumping rate, diameter and the shape of the cave, and the stability of the cave is more sensitive to the pumping rate and the diameter. The research results can provide support for disaster prevention and control in karst area.