In order to decrease the heat leak of some space used Dewar and enhance the mechanical property at the same time, Kevlar fiber which has ultra-high strength,ultra-low thermal conductivity and low density is used as the support material, and the support structure is designed at the same time. A theoretical model of the natural frequency is established and the six natural frequencies are deduced from the model using Rayleigh method. Finite element method (ANSYS) is used to compare with the computation results. Finally, the support structure under certain condition is designed and the frequency experiment is done. The theoretical results are in agreement with the simulation and the deviation between theoretical model and experimental results is smaller than 20%. Results show that the cross area, axial angle and plane angle of the Kevlar support structure have a great influence on the natural frequency, but contact point distance Ls and the pre-tightening load have less influences.