Tissue morphogenesis is driven by local cellular deformations, themselves powered by contractile actomyosin networks. While it is well demonstrated that cell-generated forces at the microscopic scale underlie a variety of local morphogenetic processes (e.g. lengthening/ narrowing 1-4 , bending 5-8 , or folding 9,10 ), how such local forces are transmitted across tissues to shape them at a mesoscopic scale remains largely unknown. Here, by performing a quantitative analysis of gastrulation in entire avian embryos, we show that the formation of the primitive streak and the associated large-scale rotational tissue flows (i.e. 'polonaise' movements 11,12 ) are integral parts of a global process that is captured by the laws of fluid mechanics. We identify a large-scale supracellular actomyosin ring (2 mm in diameter and 250 µm thick) that shapes the embryo by exerting a graded tension along the margin between the embryonic and extra-embryonic territories. Tissue-wide flows arise from the transmission of these localized forces across the embryonic disk and are quantitatively recapitulated by a fluid-mechanical model based on the Stokes equations for viscous flow. We further show that cell division, the main driver of cell rearrangements at this stage 13 , is required for fluid-like behavior and for the progress of gastrulation movements. Our results demonstrate the power of a hydrodynamic approach to tissue-wide morphogenetic processes [14][15][16] and provide a simple, unified mechanical picture of amniote gastrulation. A tensile embryo margin, in addition to directing tissue motion, could act as an interface between mechanical and molecular cues, and play a central role in embryonic self-organization.