The shape of epithelial tissue supports physiological functions of organs such as intestinal villi and corneal epithelium. Despite the mounting evidence showing the importance of geometry in tissue microenvironments, the current understanding on how it affects biophysical behaviors of cells is still elusive. Here, we cultured cells on various protruded convex structure such as triangle, square, and circle shape fabricated using two-photon laser lithography and quantitatively analyzed individual cells. Morphological data indicates that epithelial cells can sense the sharpness of the corner by showing the characteristic cell alignments, which was caused by actin contractility. Cell area was mainly influenced by surface convexity, and Rho-activation increased cell area on circle shape. Moreover, we found that intermediate filaments, vimentin, and cytokeratin 8/18, play important roles in growth and adaptation of epithelial cells by enhancing expression level on convex structure depending on the shape. In addition, microtubule building blocks, α-tubulin, was also responded on geometric structure, which indicates that intermediate filaments and microtubule can cooperatively secure mechanical stability of epithelial cells on convex surface. Altogether, the current study will expand our understanding of mechanical adaptations of cells on out-of-plane geometry.