This work exploits the concept of stabilization techniques to improve the behaviour of either mixed or pu/mixed u/εlinear/linear triangular elements when strain localization analysis is required. Different stabilization methods suitable for either Mode-I or Mode-II structural failure are proposed and compared to check the global stability of the corresponding discrete finite element formulation. Both elasto-J2-plastic and isotropic damage models have been used for the constitutive behaviour of the material. In both cases, exponential softening has been introduced in the post-peak regime. The results obtained do not suffer from spurious mesh-size or mesh-bias dependence, comparing very favorably with those obtained with standard approach.