Creep buckling analyses under varying loads are performed on a circular cylindrical shell with an initial imperfection subjected to axial compression and on a partial spherical shell under uniform pressure. The finite element method is applied to the creep deformation analysis to obtain the critical time when creep buckling occurs. The results show that a linear cumulative damage rule for creep buckling can be applied to the creep buckling of the circular cylindrical shell but cannot be applied to that of the partial spherical shell.