Embryo deformation during gastrulation is simulated using a fluid-mechanical approach. The possibility that the deformation is governed by the forces originated at the embryo surface rather than by pulling by filopodia is considered. The slow viscous flow and the deformation during in vitro exogastrulation is solved using a boundary integral equation formulation. The results show a distinct anisotropic distribution of meridional and circumferential tensions, which are capable of producing the dynamics and shape of the archenteron development. This anisotropy suggests the existence of a specific biochemical activity at particular surface regions prior to and during the gastrulation process. The mechanical model can serve as a tool to help discriminate between the possible suggested mechanisms.