Three-dimensional numerical models are developed to investigate the anti-liquefaction of ordinary (OSCs) and geosynthetic-encased (GESCs) stone columns in sandy soil under sinusoidal loading using the fluid-solid coupling method. The validated models capture and compare the vertical and radial deformation, excess pore water pressure (EPWP), and vertical effective stress of OSC, GESC, and sandy soil. Furthermore, ten essential factors are selected to conduct the parametric study. Numerical results reveal that GESC is more suitable for improving sandy soil and resisting dynamic load considering the deformation and EPWP. The bulging deformation is no longer the primary reason for failure. The partial encasement (e.g., 1-2D, D = column diameter) and short floating and end-bearing GESCs (e.g., 1-2.5D) are not recommended for reinforcing the sandy soil. GESC is more sensitive to low-frequency and high-amplitude loads, with shear and bending, whereas displays a block movement under higher frequency and lower amplitude loading. The change in loading amplitude is more disadvantageous to GESC than loading frequency. GESC with a large diameter cannot effectively resist the dynamic loads.