The embryo of the Drosophila Melanogaster undergoes a series of cell movements during its early development. Gastrulation is the process describing the segregation of the future internal tissues into the interior of the developing embryo. Gastrulation starts with the formation of the ventral furrow, a process commonly known as the ventral furrow invagination. During this process, the most ventrally located blastoderm cells flatten and progressively constrict their apical sides until they are wedge shaped. As a result of these cell-shape changes, the blastoderm epithelium first forms an indentation, the ventral furrow, which is then completely internalized. We focus on the study of the mechanisms that drive the invagination. The main questions that gave birth to this thesis are: "What is the role of the apical constriction of the ventral cells in the invagination?" and "Once the ventral cells are internalized, what is the mechanism that drives the ventral closure?" We attempt to answer to these two questions from a biomechanical point of view. For this purpose, a 3D mesh of the embryo of the Drosophila Melanogaster has been created. Based on this mesh, two "a minima" biomechanical models of the Drosophila embryo have been created, a physically based discrete model and a model based on the Finite Element Method. The results of the simulations in both models show that the geometry of the embryo plays a crucial role in the internalization of the ventral cells. The two models efficiently simulate the internalization of the ventral cells but are incapable of reproducing the ventral closure. We hypothesize that the ventral closure can be explained by the interplay of forces developed in the embryo once the internalized ventral cells undergo cell division. We propose an approach to divide elements in a Finite Element Mesh and we integrate it to the Finite Element Model of the Drosophila Melanogaster.