Many organs are formed through folding of an epithelium. This change in shape is usually attributed to tissue heterogeneities, for example, local apical contraction. In contrast, compressive stresses have been proposed to fold a homogeneous epithelium by buckling. While buckling is an appealing mechanism, demonstrating that it underlies folding requires measurement of the stress field and the material properties of the tissue, which are currently inaccessible in vivo. Here, we show that monolayers of identical cells proliferating on the inner surface of elastic spherical shells can spontaneously fold. By measuring the elastic deformation of the shell, we infer the forces acting within the monolayer and its elastic modulus. Using analytical and numerical theories linking forces to shape, we find that buckling quantitatively accounts for the shape changes of our monolayers. Our study shows that forces arising from epithelial growth in three-dimensional confinement are sufficient to drive folding by buckling.