Based on state equation that stress is the function of strain, strain-rate and temperature, the paper establishes the differential constitutive equation used for analyzing load-stability and the variational constitutive equation used for analyzing geometry-stability during superplastic tensile deformation, which contain strain hardening index, strain-rate sensitivity index, temperature sensitivity index introducted for the first time and temperature undulation index introducted for the first time in the paper. And then, based on the universal condition of plastic elementary theory, the paper analyzes load-stability and geometry-stability under continuously rising temperature and under the non-uniform temperature along the axes of specimen respectively. The results prove the impact of continuously rising speed and non-uniform value of temperature on deformation stability is that the faster temperature rises and the more non-uniform temperature is, the smaller the corresponding uniform strain of load-stability and geometry-stability are; strain hardening index is the necessary condition of stability during superplastic tensile deformation, and geometry-instability will not happen when load-instability occurs, but happen when uniform deformation has lasted after load-instability; in the superplastic temperature field, constant temperature is not necessary condition of superplasticitiy, but during the deformation, the slower temperature rises and the more uniform temperature is, the more stable deformation is. Based on state equation that stress is the function of strain, strain-rate and temperature, the paper establishes the differential constitutive equation used for analyzing load-stability and the variational constitutive equation used for analyzing geometry-stability during superplastic tensile deformation, which contain strain hardening index, strain-rate sensitivity index, temperature sensitivity index introducted for the first time and temperature undulation index introducted for the first time in the paper. And then, based on the universal condition of plastic elementary theory, the paper load load-stability and geometry-stability under continuously rising temperature and under the non-uniform temperature along the axes of marker respectively. The results prove the impact of continuously rising speed and non-uniform value of temperature on deformation stability is that the faster temperature rises and the more non -uniform temperature is, the smaller the corresponding uniform s train of load-stability and geometry-stability are; strain hardening index is the necessary condition of stability during superplastic tensile deformation, and geometry-instability will not happen when load-instability occurs, but happen when uniform deformation has lasted after-load-instability; in the superplastic temperature field, constant temperature is not necessary condition of superplasticitiy, but during the deformation, the slower temperature rises and the more uniform temperature is, the more stable deformation is.