Five flexjoints of tendon connector with different rubber material or structure were simulated by FEM to study the effect of parameters on the stiffness of flexjoint. The flexjoints were also tested under compression and rotation load. The material tests are taken on the specified rubber, and a half 3D model and a 2D model are built by Abaqus/Standard software. Neo-Hooke, Mooney-Rivlin and Yeoh constitutive model are used in the simulation. The experiments and simulation results are compared to analyze the validity and accuracy of different constitutive models, and the results show that the compression stiffness of flexjoints will increase as displacement increases, and the rotational stiffness will decrease as the angle increases. The increase in the number of the rubber layers will improve the compression stiffness but has little effect on the rotation stiffness. The results of simulation with Yeoh model can fit the experimental results very well. The Mooney-Rivlin model can also provide a relative accurate results under small deformation. The compression simulation results of Mooney-Rivlin model will be smaller than test results because that model cannot reflect the "upturn" of rubber material. The Neo-Hooke model provides the biggest error.