This document contains the result resulting from the work in the doctoral thesis Innovative mathematical and numerical models for studying the deformation of shells during industrial forming processes with the Finite Element Method. The objective of this thesis is to contribute to the development of finite element methods for the analysis of the stamping processes, an area of problems with a very clear industrial application. Indeed these kinds of problems involve multiple disciplines and require the understanding of different mechanical problems, being the most relevant disciplines the continuous mechanics, the plasticity, contact problems, among others, depending of the problematic of study.