The proposed methodology lies on the use of the adaptive mesh remeshing (AMR) technique in the context of 2D shape optimization problems analyzed by the Finite Element Method. A suitable and very general technique for the parametrization of the optimization problem, that uses B-splines to define the boundary, is first presented. Then, mesh generation, using the advancing frontal method, the error estimator and the remeshing criteria are studied in the context of shape optimization problems. Particularly, the analytical sensitivity analysis of the different items ruling the problem (B-splines, Finite Element Mesh, structural behaviour, and error estimator) is studied in detail. The sensitivities of the Finite Element Mesh and error estimator permit their projection from one design to the next one leading to an “a priori knowledge” of the finite element error distribution on the new design without the necessity of any additional structural analysis. With this information the remeshing criteria permits to build up a finite element mesh on the new design with aa specified and controlled level of error. The robustness and reliability of the proposed methodology is checked through several examples.