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This work develops an inverse procedure to identify the material parameters of meniscus behaving like hyperelastic materials. A novel objective function is proposed with two coefficients which can control the contributions for the small deformation stage and the large deformation stage in a well-balanced fashion respectively. By utilizing this, the global minimizer of material constants can be achieved for the error between the FEM solutions and the experimental data. In the experiments, a set of simple uniaxial compression tests are performed on fresh meniscal tissues, with which the anisotropic properties of the meniscal tissue have been obtained from the present inverse procedure. This research has shown that the proposed inverse procedure is stable and reliable to determine the anisotropy material constants in hyperelastic models for soft biological tissues like meniscal tissue. The objective function proposed in this paper can be extended for different types of identification problems by properly adjusting these two coefficients for different loading stages. But for deformations with more distinctive stages, more coefficients should be required in the objective function.