The Nematode Caenorhabditis elegans is one of the best studied animal model organisms in Biology. Once the oocyte has been fertilized, it develops in with an invariant pattern of cell divisions (cell lineage) into an animal consisting of exactly 959 cells with a fixed body plan. Moreover, the development of the Caenorhabditis elegans embryo can be followed at single cell resolution while the dynamic changes in gene expression are observed in real time. We will present our efforts to create the first whole embryo computational model that incorporates the current knowledge about the genetic network controlling cellular differentiation. We are using a simple syntax to describe the cell-cell interactions that give each cell in the developing embryo its specific identity. Furthermore, we are using lineage simulations to test the effects of different perturbations on the cell division pattern. Computational modeling may be used to predict how environmental changes affect a developing embryo.