Animal cells are thought to sense mechanical forces via the transcriptional co-activators YAP/TAZ, whose sole Drosophila homolog is named Yorkie (Yki). In mammalian cells in culture, artificial mechanical forces induce nuclear translocation of YAP/TAZ. Here we show that physiological mechanical strain can also drive nuclear localisation of Yki and activation of Yki target genes in the Drosophila follicular epithelium. Mechanical strain activates Yki by stretching the apical domain, reducing the concentration of apical Crumbs, Expanded, Kibra and Merlin and reducing apical Hippo kinase dimerisation. Overexpressing Hippo kinase to induce ectopic activation in the cytoplasm is sufficient to prevent Yki nuclear localisation even in flattened follicle cells. Conversely, blocking Hippo signalling in warts clones causes Yki nuclear localisation even in columnar follicle cells. We find no evidence for involvement of other pathways such as Src42A kinase in regulation of Yki. Finally, our results in follicle cells appear generally applicable to other tissues, as nuclear translocation of Yki is also readily detectable in other flattened epithelial cells such as the peripodial epithelium of the wing imaginal disc, where it promotes cell flattening.