This thesis presents the model we developed to simulate morphogenesis problems using 2D cells. The model uses a simplified representation of the cell with a detailed discretization of the cell membrane, but without internal structure. The latter is replaced by an internal pressure force, allowing modeling the evolution of the cell state. The cell membrane vertices follow Newtonian dynamics, with forces representing membrane deformation, cell contact and adhesion, and internal pressure. Biological processes are either dependent on the simulated experiment, such as the cell cycle, or fixed by the model, such as the evolution of the cell state. We validated our model for individual cells and tissues. This allowed us to reproduce biological experiments, (i) studying the impact of pressure on cells on their proliferation and (ii) exploring the movement of a tissue within a band by comparing experiments with normal cell proliferation and blocked cell mitosis.