The protein caveolin-1 (cav1) is essential in the generation of caveolae, cup-like invaginations in the plasma membrane, but the mechanism of its action remains unclear. A recent cryo-EM structure revealed an 11-mer of cav1 (the 8S complex) forming a disk with a flat membrane-facing surface, raising the question of how a flat complex is able to generate membrane curvature. We previously conducted implicit-solvent and all-atom molecular dynamics simulations, which showed the 8S complex adopting a conical shape. The ability of the conical shape to remodel membranes was assumed but could not be confirmed. Here, we simulated the complex in discontinuous membrane patches of ∼30 nm diameter on the Anton 3 supercomputer. In a 2-μs simulation, a flat POPC membrane patch acquired pronounced positive curvature (curved away from the complex), converting into a hemisphere of 21-nm outer diameter. However, when the complex was constrained to prevent the conversion into a conical shape, the membrane patch acquired slightly negative curvature. These results show that the conical shape of the 8S complex is essential for positive curvature generation. A homology model of cav3 behaved very similarly to cav1, but the two recently discovered nonvertebrate caveolins remained flat and generated pronounced negative curvature. Simulations of cav1 in 70:30 POPC:cholesterol and other cholesterol-containing mixtures showed significantly lower curvature than in the pure POPC membrane or in an E. coli membrane mimic. This appears to be caused by cholesterol flipping from the distal to the proximal leaflet. No specific binding of cholesterol to the cav1 CRAC motif was observed, nor significant enrichment of cholesterol in contact with the complex. These observations lead to the hypothesis that cholesterol is enriched in caveolae not because of specific binding to caveolin, but because it can alleviate curvature stress due to its negative spontaneous curvature and its ability to rapidly flip-flop.