The compression and torsion behavior for the three-dimensional braided C/E 4-D and 5-D circular tubes and the axial compression bearing-capacity for the Analogue Structure of Rocket Link-stage were investigated by experimental method in this paper. The experimental results show that the compression behavior for 5-D material is superior to 4-D material but the shear modulus for 5-D specimens are nearly the same with 4-D ones. The 3-cell model and FGM model are applied to predict the relative properties and compression strength of the tubes. The comparisons between the theoretical results and the experimental ones indicate that the predict results by 3-cell model are fairly coincident with the experiments, and the predict values by FGM model are lower. The results in this paper are a good basis for the designer of the braid sructures.