Abstract: Clathrin mediated endocytosis is the most widely used means of cellular trafficking and membrane bending is the first step involved. The mechanism of membrane bending is highly debated1-3 . Scaffolding is one of the mechanisms to create membrane curvature by molding the membrane into the spherical shape of the clathrin cage. However, the impact of membrane elastic parameters on the assembly and shape of clathrin lattices has neverbeen experimentally evaluated. Addressing this question, in this study, we have reconstituted clathrin budding in vitro with giant unilamellar vesicles (GUVs), purified adaptors and clathrin. By changing the osmotic conditions, we found that clathrin coats caused extensive budding of GUVs under low membrane tension, while polymerizing as a flat lattice under moderate tension. High tension and bending rigidity of the membrane fully inhibited polymerization. Theoretically, we predicted the tension values for which transitions between different shapes of clathrin coats occur. We further measured thechanges in membrane tension during clathrin polymerization, and used our theoretical framework to estimate the polymerization energy from these data. Our results show that membrane tension controls clathrin-mediated budding by varying the membrane budding energy. The measured membrane tension and clathrin polymerization energy were found to be of the same order as in vivo tension regimes, suggesting a physiologically critical control of the shape of clathrin mediated budding by membrane elasticity.