Gas hydrates have great potential as future energy resources. Several productivity and stability analyses have been conducted for the Ulleung Basin, and the depressurization method is being considered for production. Under depressurization, ground settlement occurs near the wellbore and axial stress develops. For a safe production test, it is essential to perform a stability analysis for the wellbore and hydrate-bearing sediments. In this study, the development of axial stress on the wellbore was investigated considering the coupling stiffness of the interface between the wellbore and sediment. A coupling stiffness model, which can consider both confining stress and slippage phenomena, was suggested and applied in a numerical simulation. Parametric analyses were conducted to investigate the effects of coupling stiffness and slippage on axial stress development. The results show that shear coupling stiffness has a significant effect on wellbore stability, while normal coupling stiffness has a minor effect. In addition, the maximum axial stress of the well bore has an upper limit depending on the magnitude of the confining stress, and the axial stress converges to this upper limit due to slipping at the interface. The results can be used as fundamental data for the design of wellbore under depressurization-based gas production.