Epithelial folding transforms simple sheets of cells into complex three-dimensional tissues and organs during animal development. Epithelial folding has mainly been attributed to mechanical forces generated by an apically localized actomyosin network, however, contributions of forces generated at basal and lateral cell surfaces remain largely unknown. Here we show that a local decrease of basal tension and an increased lateral tension, but not apical constriction, drive the formation of two neighboring folds in developing Drosophila wing imaginal discs. Spatially defined reduction of extracellular matrix density results in local decrease of basal tension in the first fold; fluctuations in F-actin lead to increased lateral tension in the second fold. Simulations using a 3D vertex model show that the two distinct mechanisms can drive epithelial folding. Our combination of lateral and basal tension measurements with a mechanical tissue model reveals how simple modulations of surface and edge tension drive complex three-dimensional morphological changes.