The elastic behavior analysis of post-buckling of the frames is complex. When a frame is exerted force over critical load, it begins large deformations. In this case, the theory of small deformations is not valid for the structure, and it must be used the theory of large deformations. Post-buckling analysis of the elastic structures always requires solving method with a set of nonlinear differential equations based on equilibrium equations. In designing the members under the axial force or the axial force and the bending moment in the structure, in addition to the yielding criterion, the buckling criterion is important too. However, if the length of the member is too much or the member is slender, before yielding, buckling occurs in the member, which requires the member to be checked for possible buckling. In this research, the post-buckling behavior of the lateral unbraced frame is analyzed with the help of Elastica theory. For this purpose, the first step is to analyses a cantilever column by the Maclaurin Series method. By examining the results of the post-buckling behavior of this column with the previous research, the verification of this method has been evaluated. In the following, due to the verification of the method, the large deformations and post-buckling behavior L-shaped frame are investigated. To analyses the frame, it is necessary to solve a nonlinear equation system. The Maclaurin Series method has been used to obtain nonlinear equations. With the help of the equations, the frame deformations diagrams have been plotted. Mathematica software is used to draw charts and solve nonlinear equations. In the following, with the modelling of the frame in Finite Element ABAQUS software, the comparison of the accuracy of the software results with this analysis has been checked and the convergence of the responses has been examined.