Brief development process of the finite element method, foundation of quasi-conforming element has been analyzed from weak formulation generalized compatibility equations and its weak continuity condition in this paper. The quasi-conforming element methods are the exact solution of generalized compatibility equations and satisfy the weak continuity requirement naturally. The quasi-conforming element methods do not satisfy stress equilibrium conditions and concision calculating process of matrix’s athwart. The discrete precision can be predicted in prior. It also extends space of original finite element method and is landmark in computational mechanics.