<p>The recent discovery of the flat, disc-like structure of caveolin oligomers, predicted to be embedded in one membrane leaflet, has challenged earlier models of membrane curvature generation by caveolins during caveola biogenesis. Here, we provide a mechanism for this phenomenon. We propose that the central factor behind the membrane shaping by caveolin discs is a difference in interaction energies of the membrane leaflets with each other and with the hydrophobic faces of the caveolin discs. We demonstrate, through computational analysis, that the caveolin disc embedding induces elastic stresses of tilt and splay in the membrane leaflets, which, in turn, drive membrane kinking along the disc boundaries. The predicted resulting membrane shapes have an overall curved and faceted appearance in agreement with observations. Our model also provides a mechanistic understanding of the role of the negative intrinsic curvatures of lipids such as cholesterol and diacylglycerols, in caveola assembly.</p>