The unique structure of kidney tubules is representative of their specialized function. Because maintaining tubular structure and controlled diameter is critical for kidney function, it is critical to understand how topographical cues, such as curvature, might alter cell morphology and biological characteristics. Here, we examined the effect of substrate curvature on the shape and phenotype of two kinds of renal epithelial cells (MDCK and HK-2) cultured on a microchannel with a broad range of principal curvature. We found that cellular architecture on curved substrates was closely related to the cell type–specific characteristics (stiffness, cell–cell adherence) of the cells and their density, as well as the sign and degree of curvature. As the curvature increased on convex channels, HK-2 cells, having lower cell stiffness and monolayer integrity than those of MDCK cells, aligned their in-plane axis perpendicular to the channel but did not significantly change in morphology. By contrast, MDCK cells showed minimal change in both morphology and alignment. However, on concave channels, both cell types were elongated and showed longitudinal directionality, although the changes in MDCK cells were more conservative. Moreover, substrate curvature contributed to cell polarization by enhancing the expression of apical and basolateral cell markers with height increase of the cells. Our study suggests curvature to be an important guiding principle for advanced tissue model developments, and that curved and geometrically ambiguous substrates can modulate the cellular morphology and phenotype.