The latest study for formulation of finite element method and computation techniques has progressed widely. The classical method in the formulation of frame elements for geometrically nonlinear analysis derives the geometric stiffness directly from the governing differential equation for bending with axial force. From the computational viewpoint of this paper, the most common approach is the finite element method. Commonly, the formulation of frame elements for geometrically nonlinear structures is based on appropriate interpolation functions for the transverse and axial displacements of the member. The formulation of flexibility-based elements, on the other hand, is based on interpolation functions for the internal forces. In this paper, a new method is used to suppose that interpolation functions for the displacements from the curvatures is Lagrangian interpolation. This paper derives flexibility matrix from that displacement functions and is considered the application of it. Using the flexibility matrix, this paper apply the program considered geometrically nonlinear analysis to common problems.