The mechanical aspects of embryonic morphogenesis have been widely analysed by numerical simulations of invagination in sea urchins and Drosophila gastrulation. Finite element models, which describe the tissue as a continuous medium, lead to the global invagination morphogenesis observed in vivo. Here we develop a simulation of multicellular embryo invagination that allows access to both cellular and multicellular mechanical behaviours of the embryo. In this model, the tissue is composed of adhesive individual cells, in which shape change dynamics is governed by internal acto-myosin forces and the hydrodynamic flow associated with membrane movements. We investigated the minimal structural and force elements sufficient to phenocopy mesoderm invagination. The minimal structures are cell membranes characterized by an acto-myosin cortical tension and connected by apical and basal junctions and an acto-myosin contractile ring connected to the apical junctions. An increase in the apical–cortical surface tension is the only control parameter change required to phenocopy most known multicellular and cellular shape changes of Drosophila gastrulation. Specifically, behaviours observed in vivo, including apical junction movements at the onset of gastrulation, cell elongation and subsequent shortening during invagination, and the development of a dorso-ventral gradient of thickness of the embryo, are predicted by this model as passive mechanical consequences of the genetically controlled increase in the apical surface tension in invaginating mesoderm cells, thus demonstrating the accurate description of structures at both global and single cell scales.