There were often happened cases for beam elements with initial stress or initial strain while the geometrically nonlinear analysis was performed for the plane structure. The deduction of stiffness matrices was awfully difficult because the nonlinear stiffness matrices included node displacement vectors and extensive matrix operations. Based on the nonlinear geometric equation of plane beam element and general elastic relationship of stress-strain including initial stress and initial strain

the tangent stiffness matrix was derived. All explicit formula of stiffness matrices including initial stress and strain item have been developed by use of the MATLAB Mathematical Tools. The results are of great significance to the nonlinear finite element programming for plane beam elements.