One of the schemes most broadly used in the industry of production of parts to carry out the quality control of the produced pieces consists on making a comparison of such pieces against an ideal prototype denominated CAD model of the piece. To carry out this comparison, experimental data of the surface of the piece are acquired and a rigid alignment among the model generated from these data and the CAD model of the piece is carried out. Although current systems consider only rigid pieces to be inspected, there are numerous pieces for which this alignment process is not enough because the shape of such pieces changes when they are assembled. In this article a new method of non rigid alignment is presented, based on the use of radial basis functions, which allows to improve the inspection process of deformable pieces based on CAD. Results of the application of the method on several deformable models are presented.