There is increasing evidence that animal morphogenesis consists of a large scale tissue flow, which defines the gross characteristics of the animal body at a very early developmental stage. We have studied the vertebrate embryo cell trajectories between a moment when it is flat and formless, to a moment when the body plan is recognizable (chicken embryo days 2-3 of development). We find that a large vortex flow patterns the vertebrate and especially the limb territories, both hindlimbs and forelimbs. In vivo velocity measurements show that the vortices are dragged by a localized shear oriented along the median axis. A simple hydrodynamic model accounts for the lenticular shape of the limb plates. On the hindlimb plate, the flow propagates in the form of a solid-body vortex on the limb plate, dragged by a Poiseuille flow along the backbone. In vivo tonometry measurements show that there exist stress gradients in the embryonic tissue, and that the flow pattern is congruent with the direction of decrease of stress magnitude.