Ventral furrow invagination is the initial step of gastrulation, early stage of embryogenesis. This paper focuses on the study of the connection between the apical constriction of the ventral cells and the initiation of the invagination. For this purpose, we have created a 3D biomechanical model of theembryo of the drosophila melanogaster based on the Finite Element Method. Each cell is modeled by an elastic hexahedron and is firmly attached to its neighboring cells. A uniform initial distribution of elastic and contractile forces is applied to the cells along the model. The numerical simulations show that the invagination starts at the ventral curved extremities of the embryo and then propagates to the ventral medial layer. Our theory is that this observation can be attributed uniquely to the specific shape of the blastula and we provide mechanical evidence to support this theory. The study of individual cells also reveals details concerning cell deformation and motion. We use it to monitor the depth of the ventral furrow, the surf ace/volume ratio of a ventral cell and the time after which the cell constriction stops. Finally, the model is enhanced in order to study, from a biomechanical point of view, the displacement of the centrosome of a constricting cell in relation tothe cytoskeletal forces. The results are compared with in vivo studies of the phenomenon to determine the efficiency of our model and to provide an insight as to whether the biomechanical approach can be enhanced in order to aid the explanation of other embryogenetic processes as well.