Abstract: Although there are a lot of research achivements for co-rotational procedure of a 2D quadrilateral element, most of these elements were based on geometric consisitency and produced a symmertric element tangential stiffness matrix. For elements of field consistency, there are less research works so far. Based on the field consistency principle of co-rotational procedure, a simple tangent stiffness matrix for the 2D quadrilateral element under large rotation with small strain is proposed in this paper. Comparied with the symmetric tangential stiffness matrix of geometric consistency, the element tangential stiffness matrix is asymmetric but less of computation. In nonlinear computation, this is positively meaningful as the round off errors accumulate with the increase of computation of element stiffness matriecs and consequently lead to the possibility of iteration disconvergence. In collaboration with the proposed asymmetric element stiffness matrix, an unified incremental iteration scheme of combining displacement increamental method and load increamental method is employed for the solution of resulting nonlinear FEM equations and following the procedure mentioned above and its corresponding formulation, a FORTRAN computer program, named NSAP, has been developed. Computations and analysis for plane beams and arches have verified the correctness of the element’s formulation, the high efficency of the program and the strong nonlinear computation ability of the method. It is cable of analyzing nonlinear behavior of planar stress of beams and arches. Computations presented reflect preferably a comprehensive understanding of geometrical nonlinear characteristics of beams and arches, could be beneficial for the engineeing designers.