By using the semi-inverse solving methods, I.Elishakoff and Lei Wu et al.have researched the single mode in-verse problems for axially functionally graded inhomogeneous beams before .They discussed the conditions and methods about re-constructing the axial flexure stiffness coefficients or linear density function when the cross -section area is constant and the linear density function or axial flexure stiffness coefficient is given polynomial .Lei Wu et al.have discussed the positivity problem of ob-tained flexure stiffness coefficient also .These researched achievements obtained scientist ’ s sufficient attention but have some defi-ciencies also.Based on these cases, we review the obtained achievements and point out being problems in this paper .And we ex-pect this researched direction also.%文献报道了采用半逆解法研究非匀质材料纵向功能梯度梁的单模态逆问题，具体讨论了当梁的横截面积为定值而材料线密度或抗弯刚度为已知多项式时，如何求解梁的多项式型抗弯刚度系数或材料线密度的条件和方法，及所得轴向抗弯刚度系数的正值性。这些研究成果获得了学界的高度重视，但也存在某些不足。本文就此研究成果做一回顾，指出存在的问题，展望今后的研究方向。
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