Despite the knowledge of the behavior of structures on elastic base being important for the engineering of general form, the motivation of this work is focused in the Biomechanics, in our works involving the group of research of the Clinic of the Dr.Ivo Pitanguy and the Saint Casa de Misericórdia. In recent thesis of Dsc., a modeling of the surgical technique of expansion of the skin was carried through. The expansion of the skin is a physiological process, defined as the capacity that the skin has to increase its superficial area in reply to an imposed deformation. During the expansions it could be observed that depending on the region where the expander is implanted its behavior could be sufficiently distinct. Expanders who are implanted on the head initiate the expansion of the skin immediately when the saline solution is introduced in the expander. When the expander is implanted in regions with more fat, as for example in the thigh, the expansion of the skin does not initiate immediately in view of that the expander is deformed to the inner part, pressuring the fat (that offers little resistance) and not the skin. This behavior causes opening of the points in the scar and can make impracticable the process of expansion in that region. For the simulation the process of skin expansion, it was made an expansion with rubber sheet and a set was used for the elastic base that consisted of a filled elastic bladder with a viscous material in its interior. This work is pioneer in investigating numerical and experimentally the behavior of the rubber sheet expansion on rigid base and elastic base, comparing its behavior. The numerical and experimental results of the expansion of the rubber sheet had a good agreement and the parametric analysis of the thickness of the rubber sheet proved the importance of a precise measure of the skin thickness by the doctors, since the verified pressures are different for each thickness. Diverse constituent equations had been studied, looking the one that better described the process of the expansion of the skin. The formularization of the Neo-Hook material got the best results for the rubber sheet. Also a study with the formularization of energy of Delfino was made to study the expansion of the human skin.