Abstract
In this paper we study the asymptotics of the three‐dimensional displacement field for clamped and free linear elastic shallow shells as the thickness tends to zero. As in the case of plates, the asymptotics contains regular terms and boundary layers. The two‐dimensional generators of the regular parts are solutions of two‐dimensional problems governed by an elliptic system in the sense of S. Agmon, A. Douglis and L. Nirenberg. This asymptotics is justified by optimal error estimates and improves the results obtained by S. Busse, P.G. Ciarlet and B. Miara.