Abstract: Due to the hoop effect of geogrids, the stress and deformation mechanism of geosynthetic-encased stone columns (GESCs) is more complex than that of the ordinary stone columns. In this study, the stress and deformation of a single GESC is regarded as a space axisymmetric problem. Based on the symplectic system theory, a symplectic dual equation considering the shear stress of the cross section of the column is formulated, the variables of the equation are separated, and the distribution functions for the settlement and radial deformation of GESCs are finally obtained according to the boundary conditions. The rationality and feasibility of this method are verified by the practical example, and the parameter analysis shows that the settlement and bulging of GESCs decrease with the increase of encasement stiffness. They increase with the increase of pile-soil stress ratio, but the growth rate decreases gradually. They decrease with the increase of encasement depth, but no longer change when they exceed the optimal encasement depth. The optimal encasement depth increases with the increase of load and pile spacing, and with the decrease of lateral pressure coefficient.