Abstract: Although many plane beam elements of large rotation have been developed, much of these early works were surprisingly sophisticated and worth improvement. Starting from geometric and physical relations of the plane frame, this work successfully applied co-rotational procedure to derive non-linear asymmetric tangent stiffness matrix of plane beam element under large but small-strained rotational displacement. Nonlinear finite element iteration procedure is also established by the Newton-Raphson technique, and a corresponding FORTRAN program NPFSAP completed. Numerical analysis results of high accuracy for beams, square and circular frames of large rotational displacement are thus computed and obtained. Computations indicate that formulations for the nonlinear element are of higher performance and validation, and that the nonlinear solution procedures are of rapid and stable convergence. The method and its program NPFSAP could be helpful for engineering designers to analyze beam and frame structures more accurately.