Understanding the geometric, topologic, and mechanical properties of cells and their interactions is critical for studying tissue pattern formation and organ development. Computational model and tools for simulating cell pattern formation have broad implications in studying embryogenesis, blood-vessel development, tissue regeneration, and tumor growth. Although a number of cell modeling methods exist, they do not simultaneously account for detailed cellular shapes as well as dynamic changes in cell geometry and topology. Here we describe a dynamic finite element cell model (dFEMC) for studying populations of cells and tissue development. By incorporating details of cell shape, cell growth and shrinkage, cell birth and death, cell division and fusion, our method can model realistically a variety problems of cell pattern formation. We give two examples of applying our method to the study of cell fusion and cell apoptosis. The dFEMC model developed here provides a general computational framework for studying dynamics pattern formation of tissue.