High altitude balloon provides a reliable platform for high altitude scientific experiments. The shape of the balloon is directly related to the whole process of making and flying. The multiple-shooting method was combined with the sequence of two quadratic programming method, and the under-expansion shape and optimum-expansion shape were obtained. In addition, the finite element method was used to analyze the stability and stress and strain of the sphere to verify the correctness of the derived sphere. On this basis, the sensitivity analysis and related application of the key parameters affecting the balloon shape were carried out, and the effects of balloon load, flight altitude and temperature difference between day and night on the balloon shape were obtained quantitatively.