As the dynamic responses of casing stress was still far from clear, this paper aimed at proposing a mechanical analysis method for investigating 3D stress temporal-spatial distribution of the casing in hydrate production well. In the proposed approach, a coupling 3D model and the corresponding algorithm were developed by combining mathematical models of hydrate decomposition front and reservoir parameters. Simulation results revealed that casing stress reached the maximum at the depressurization area, and as production advanced, it increased first and then gradually stabilized. As production pressure, depressurization area and initial hydrate saturation changed from 6MPa to 2MPa, 4m to 8m and 48% to 28%, casing stress increased by 58.8%, 12.6% and 20.6%, respectively.