In this work shall be presented a stabilized finite element method to deal with incompressibility in solid mechanics. A mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields. To overcome the Ladyzhenskaya-Babuska-Brezzi condition, a stabilization technique based on the orthogonal sub-grid scale method is introduced. The main advantage of the method is the possibility of using linear triangular finite elements, which are easy to generate for real industrial applications. Results are compared with several improved formulations, as the enhanced assumed strain method (EAS) and the Q1P0-formulation, in nearly incompressible problems and in the context of linear elasticity and J2-plasticity.