Abstract: Based on general solution for the homogeneous governingequation for the linear buckling analysis of Euler beam, new shape functionsare constructed and a new finite element is formulated. With the derivedelement stiffness matrix and geometric stiffness matrix, an iterativealgorithm based on conventional eigenvalue calculation procedure is proposedfor linear buckling analysis of frame structures. The conventional finiteelement is proved to be an approximation of the proposed element. By theapplication of the proposed element and algorithm, exact buckling solutionsof frame structures can be obtained even with coarse meshes. Illustrativenumerical examples are presented to show the effectiveness of the newelement and algorithm.