Parametrical models have become an important mathematical tool for free form curves and surface description. they allow the use of state-of-the-art computers to do the various processing and analysis with respect to shape (calculation of the volume and surface area, vibration analysis, NC programs preparation, etc.). Without these models, the current product design and manufacturing would be difficult. The paper presents an analysis study for the most important parametrical models of free form curves and surfaces description (Ferguson, Coons, Bezier, B-Spline and rational models). Firstly, it emphasises external and mathematical properties of each model. Secondly, it gives the most interesting interfaces between models. Thus the process of complex surface design and manufacturing would be more efficient in view this analysis. Finally for validation, the study is ended by an application to the design of a car bonnet.Parametrical models have become an important mathematical tool for free form curves and surface description. they allow the use of state-of-the-art computers to do the various processing and analysis with respect to shape (calculation of the volume and surface area, vibration analysis, NC programs preparation, etc.). Without these models, the current product design and manufacturing would be difficult. The paper presents an analysis study for the most important parametrical models of free form curves and surfaces description (Ferguson, Coons, Bezier, B-Spline and rational models). Firstly, it emphasises external and mathematical properties of each model. Secondly, it gives the most interesting interfaces between models. Thus the process of complex surface design and manufacturing would be more efficient in view this analysis. Finally for validation, the study is ended by an application to the design of a car bonnet
