The main objective of this paper is to present results on the lateral buckling of beams using finite elements based on Kirchhoff and Mindlin-Reissner Plate theories, merged with membrane elements in order to include the analysis of shells. A MATLAB code was developed to calculate static and dynamic critical loads, buckling modes, frequencies, and vibration modes of thin and thick plates subjected to conservative and non-conservative (also called follower or circulatory) loads. Mass and stiffness matrices are employed to determine natural frequencies. In the case of conservative loads, static critical loads are calculated by adding a so-called geometric matrix. However, in case of displacement-dependent applied forces, it is necessary to implement a matrix that will correct the loads, designated as load matrix. In the case of conservative forces, the load matrix is symmetric, and in the case of non-conservative forces, it is non-symmetric. In the latter case, the critical load usually will correspond to dynamic behavior designated as flutter. Different boundary conditions and loads are considered and several cases of lateral buckling are investigated. Theoretical values when found in the literature are compared with values determined by Finite Element Method (FEM). The lateral instability of slender beams is very important in practice, because in some situations it may occur prior to ultimate plastic limit state in bending. Therefore, lateral buckling is mentioned in a wide variety of national and international rules, and some comparisons with the results of the computer code developed herein are presented.