Considering advantages of generalized finite element and rational finite element a kind of quadrilateral elements (generalized element) is developed for plane-strain problem. The element includes Poisson's effect. Additional terms of displacement mode inside element are constructed according to semianalytical solution of node displacement degrees of freedom constraint elastic plane strain equation. The element reflects real displacement field accurately and elemental calculation accuracy was improved. Shape functions of generalized elements and generalized isoparametric elements are constructed and patch test and numerical tests are designed to verify calculation accuracy. Numerical tests indicate that whether in regular or irregular grid new element has higher accuracy than conventional element and generalized element. The element is convenient for implementation, which is suitable for practical engineering.