In this paper a short introduction to the finite element method is given in. The paper also contains descriptions of linear and nonlinear analysis, and analysis of heat conduction and dynamic loads and vibrations. For nonlinear analysis the best known iterative methods are listed, and the causes of the nonlinear behavior in the form of geometric and material nonlinearities in the case of bending the wire, and on supported I-beam with a continuous load in the first example and load by force and torque in the second, and the problem of gaps and contacts are explained. The paper presents examples of linear and nonlinear analysis, and analysis of contacts. Material with linear hardening and linear elastic-perfectly plastic material are used in examples of nonlinear analysis. All examples were made in the software Ansys 16.0. The analyzes were carried out and the convergence solutions of maximum displacement and the equivalent von Mises stress for different sizes of the final elements that are displayed in tables and diagrams. Solution results of given examples of wire and I-beam demonstrate that there is a risk of yielding in all cases and that these examples are needed to reinforce. Comparison of the obtained solutions for linear and nonlinear analysis are displayed in diagrams, which shows that the results of stress with linear analysis is significantly higher, because in its analysis does not use the material flow. The comparison still shows that displacement in nonlinear analysis is higher because the flow of material causes greater strain. In the case of smaller loads when the material does not exceed the limit flow, nonlinear analysis would clearly indicated, while for linear analysis stress could still be large, it is not necessary to spend extra material. Using nonlinear analysis in these cases to avoid over-dimensioning and also got a better product.