Abstract: It is difficult and has been research focusto improve the accuracy and performance of the low order elements widely usedin non-linear FEM analysis using incompatible mode. In this paper, the basic principles of EAS(The Enhanced Assumed Strain) method are systematically summarized, and the conditions toguarantee calculation convergence, the solution stability and the construction methods of theenhanced assumed strain interpolating function are elaborated in detail. The research methods andachievements about the incompatible mode geometrically non-linear FEM inChina are reviewed, which include: 1) a convergence criteria of incompatible mode geometrically non-linear FEMwas proposed based on Hellinger-Reissner generalized variationalprinciple, and the simplified modelof incompatible geometrically non-linear FEM was constructed by using some simplifiedmethods; 2) a class of non-linear generalized variational principles wasproposed, in which thecompatible conditions between elements are relaxed. The incompatible models can be constructedby selecting incompatible functions without satisfying compatible conditions prior and theconvergence can be guaranteed. The C1 or C0 geometrically non-linear generalized hybrid elements,C1 or C0 refined hybrid elements and directly refined stiffness methodscan be constructed by applying thenon-linear generalized variational principles. The problems with respectto the application of EAS methodin the non-linear FEM analysis are pointed out, that is, the restriction of constitutive lawsand the solving methods. Furthermore, the application prospect of the incompatible modenon-linear FEM is discussed.