The present project is concerned with the study of the most recent numerical simulations for structural optimization problems in aeronautics. Different techniques will be studied in order to solve non-linear constrained optimization problems with non-convex domains. In addition, the Finite Element Method will also be applied to handle the elastostatic behavior of structures. The computational implementation of numerical methods will be carried out by the well-known programming environment MATLAB. Examples of benchmarks, validation and aeronautical applications will be considered. The last part of this project will focus on the optimization of an aircraft structure using structural optimization techniques.