Equilibrium positions of a solid in large deformations. We investigate equilibrium positions of a solid in large deformations. We take the party that a solid can flatten in a solid with a lower dimension. A structure flattened by a power hammer is an example of such a situation. Moreover, we take into account the spacial variations of rotation matrix. We prove that under reasonable assumptions, there exist equilibrium positions which may be non-unique. To cite this article: M. Fremond, C R. Acad Sci. Paris, Ser. I347 (2009). (C) 2009 Academie des sciences. Publie par Elsevier Masson SAS. Tous droits reserves.