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The organization of epithelial tissues with precise spatial definition is essential to various biological processes and to generate curved epithelial structures. However, the regulation of the architecture and dynamics of collective epithelial assemblies by the matrix curvature remains understudied. Here, we photopolymerize microwells of various diameters in hydrogels to form curved epithelial structures such as breast epithelial lobules, and study how in-plane and out-of-plane curvatures modulate the mechanoresponse of epithelial tissues. In-plane curvature governed by the microwell radius drives the centripetal orientation of cells and nuclei close to the edge of the microwell, resulting from contractile forces exerted by a supracellular actomyosin purse-string. Convex out-of-plane curvature imposed at the microwell entrance leads to a vertical orientation of the nuclei towards the microwell axis. We demonstrated that increasing the out-of-plane curvature leads to more flatten and elongated nuclear morphologies with high levels of compacted chromatin. Epithelial cells exhibit higher directionality and speed around the microwell edge, demonstrating that the out-of-plane curvature significantly enhances the cellular trafficking. These findings demonstrate the importance of in-plane and out-of-plane curvatures in epithelial organization and how both can be leveraged to facilitate the engineering of curved structures to study curvature-dependent mechanotransduction pathways.