The development and maintenance of tissues and organs depend on the careful regulation and coordinated motion of large numbers of cells. There is substantial evidence that many complex tissue functions, such as cell division, collective cell migration and gene expression, are directly regulated by mechanical forces. However, relatively little is known about how mechanical stress is distributed within a tissue and how this may guide biochemical signalling. Working in the framework of a popular vertex-based model, we derive expressions for stress tensors at the cell and tissue level to build analytic relationships between cell shape and mechanical stress. The discrete vertex model is upscaled, providing exact expressions for the bulk and shear moduli of disordered cellular networks, which bridges the gap to traditional continuum-level descriptions of tissues. Combining this theoretical work with new experimental techniques for whole-tissue stretching of Xenopus laevis tissue, we separate the roles of mechanical stress and cell shape in orienting and cueing epithelial mitosis. We find that the orientation of division is best predicted by the shape of tricellular junctions, while there appears to be a more direct role for mechanical stress as a mitotic cue.