Morphogenesis is an eminently three-dimensional process, during which an organism undergoes complex deformations to acquire a given shape and organisation. The genetic patterning of Drosophila embryos and the way it regulates the expression of key molecules such as myosin, which can generate local mechanical action, has been well described. However, the way this integrates at the scale of the embryo to drive morphogenetic movements is still to be characterised. Understanding this requires us both to express locally the link between myosin activation and mechanical behaviour, and to calculate globally the resulting force balance and deformations. Axis extension in Drosophila is a good model system for this, since it involves a very large deformation of the whole of the embryo and is crucially dependent on a well characterised anisotropic myosin recruitement pattern. This paper specifically investigates whether this expression pattern causes the observed morphogenetic movement directly or only via the cell intercalation process. Our prediction of local mechanical behaviour is based on a rheological law which we have recently validated for cortical actomyosin and extend to the case when myosin generates an anisotropic prestress. In order to resolve the stresses and deformations that this produces at the scale of the whole embryo, we develop a novel finite element technique which allows us to solve the three-dimensional mechanical balance resulting from a given global distribution of myosin-generated prestress. Because axis extension is observed to involve in-plane tissue flows, the mechanical problem is expressed as a tangential flow of an emergent fluid on the curved three-dimensional surface of the embryo. Numerical simulations confirm that the planar-polarised arrangement of myosin in the germband can trigger embryo-scale flows which are qualitatively similar to those observed experimentally. Interestingly, this mechanical behaviour is shown not to rely necessarily on cell intercalation, but rather on the anisotropy of myosin action, which is known to be a major cause of intercalation in general but can also cause cell elongation. We also show that the mechanical balance that leads to axis extension towards posterior is crucially dependent on the geometry of the whole embryo, and specifically on the presence anteriorly of the cephalic furrow, which can act as a guide for morphogenetic movements. This is thus an instance when a prior morphogenetic event, cephalic furrow formation, can modify the mechanical feedback on actomyosin thanks to the geometric dependence of mechanical balance, thus having a cascading influence on further development.