  We study theoretically the shapes of a dividing epithelial monolayer of cells
lying on top of an elastic stroma. The negative tension created by cell
division provokes a buckling instability at a finite wave vector leading to the
formation of periodic arrays of villi and crypts. The instability is similar to
the buckling of a metallic plate under compression. We use the results to
rationalize the various structures of the intestinal lining observed \emph{in
vivo}. Taking into account the coupling between cell division and local
curvature, we obtain different patterns of villi and crypts, which could
explain the different morphologies of the small intestine and the colon.
