The motor protein non-muscle myosin II is a major driver of the movements that sculpt three-dimensional organs from two-dimensional epithelia. The machinery of morphogenesis is well established but the logic of its control remains unclear in complex organs. Here we use live imaging and ex vivo culture to report a dual role of myosin II in regulating the development of the Drosophila wing. First, myosin II drives the contraction of a ring of cells that surround the squamous peripodial epithelium, providing the force to fold the whole disc through about 90°. Second, myosin II is needed to allow the squamous cells to expand and then retract at the end of eversion. The combination of genetics and live imaging allows us to describe and understand the tissue dynamics, and the logic of force generation needed to transform a relatively simple imaginal disc into a more complex and three-dimensional adult wing.