The intrinsic genetic programme of a cell, combined with biochemical signals received from the environment, is not always sufficient to explain the cell’s activities. Instead, mechanical properties of the environment and mechanical stimuli are increasingly being recognized as determinants of a cell’s behavior. In the epithelial folding event that constitutes the beginning of gastrulation in Drosophila, and specifically of the invagination of the mesodermal primordium, the genetic programme of the future mesoderm leads to the establishment of a contractile actomyosin network that triggers apical constriction of cells, and thereby, furrow formation. However, some cells do not constrict but instead stretch, even though they share the same genetic programme as their constricting neighbours. We show here that their behaviour is not determined only by their genetic programme, but also by tissue-wide interactions. Being passively stretched by contracting neighbours prevents constriction even when an otherwise sufficient amount of apical, active actomyosin has been accumulated.