In this Note, we present and analyze a new method for approximating linear elasticity problems in dimension two or three. This approach directly provides approximate strains, i.e., without simultaneously approximating the displacements, in finite element spaces where the Saint Venant compatibility conditions are exactly satisfied in a weak form. To cite this article: P.G. Ciarlet, P. Ciarlet, Jr., C. R. Acad. Sci. Paris, Ser. I 346 (2008). © 2008 Académie des sciences.