This work presents three kinds of techniques for collapse analysis using the finite element method: linear buckling analysis, nonlinear buckling analysis and full nonlinear analysis. The linear buckling analysis requires the definition of an eigenvalue problem using a stiffness matrix formulation based on the initial configuration of the structure and under the assumption of a linear elastic material behavior. In the case of nonlinear buckling analysis, the eigenvalue problem was formulated employing an incremental stiffness matrix in order to consider the effects of large displacements and nonlinear material properties in the critical load estimation. Finally, the full nonlinear analysis takes into account the deformed configuration and the nonlinear material properties of the structure, updating both of them through all the incremental-iterative process up to reaching the critical load. A Finite Element computational program, using plane stress isoperimetric bidimensional elements, was developed to study the three analysis techniques applied to plane structures such as beams, columns, frames and arches. The deformed configuration of the structure, due to large displacements and rotations, was considered through the Total Lagrangian formulation, whereas the inelastic material behavior was modeled using the Von Mises plasticity model with isotropic hardening. The examples presented in this article show the influence of geometric and material nonlinearity in the critical load estimation and the postcritical behavior, being this the reason for the potential occurrence of bifurcation points over the fundamental equilibrium path defined in the load-displacement space.