The aim of this work is to develop a simultaneous smoothing-untangling procedure for parametrized surfaces. To this end we will extend the definition of the quality metrics for planar meshes to parametrized surface meshes. Then, we will develop a minimization approach on the parametric space that will allow smoothing and untangling the surface mesh. To this end, first we will increase the robustness of the standard untangling techniques. Then, we will focus on the improvement of the computational efficiency of the developed approach. Finally, several examples will be presented in order to illustrate the capabilities of the proposed method.. L'objectiu d'aquest projecte és la millora de la qualitat de malles d'elements finits generades sobre superficies paramètriques. Aquestes malles podran estar formades per triangles o quadrilàters. Aquesta millora es realitzarà mitjançant la minimització numèrica d'una mesura de la qualitat de la malla definida en l'espai paramètric