We address a classical mystery of developmental biology : how does a cell in an organ know what overall size the organ has ? According to the current paradigm, the Drosophila wing disc grows robustly to the right size because its cells respond to both signalling proteins (morphogens) and mechanical stress. Due to the long-range nature and directional dependence (anisotropy) of stress, we hypothesize that size regulation can be achieved if cells respond exclusively or primarily to stress. To test this, we develop a morpho-elastic continuum mechanical model of the wing disc in which tissue stretching stimulates cell proliferation, whereas compression inhibits it. Our model relies on the local coupling of growth and the deviatoric (traceless) part of the stress tensor, as well as a homeostatic pressure. The predictions of our model are consistent with a number of experimental observations : the spatial uniformity of cell proliferation in the wing disc, a buildup of compression in the disc center and tension in the periphery during development, and a sigmoidal evolution of the disc size which approaches a final size. To ensure that the same final size is reached even if initial conditions are perturbed, we show that the addition of a basal growth term is necessary, producing a robust encoding of the final size. Our results suggest that local mechanical feedback, which previously was assigned at most a supporting role in size regulation, may be the primary mechanism in obtaining the final disc size.