Epithelial invagination converts flat sheets of cells into three-dimensional structures — an essential process during animal development. A major mechanism of invagination is apical constriction driven by actomyosin contraction. This study reveals that invagination also requires cell rounding, which occurs when cells enter mitosis. Live imaging of the Drosophila melanogaster tracheal placode showed that the transition from an initial slow phase of invagination to a second faster phase was impaired for mutants in which cells fail to enter mitosis. Interestingly, this acceleration was not affected by treatment with a microtubule inhibitor that arrests the cell cycle after cell rounding. Thus, cell rounding, but not cell division, is required for this morphogenetic switch. Furthermore, the authors show that cell rounding functions in conjunction with epidermal growth factor receptor (EGFR)-induced myosin II contractility in surrounding cells.