An epithelium is a sheet of constantly growing cells that strongly adhere to their neighbors. Studying mechanisms that regulate the growth of epithelium is important for both understanding of development in general and finding solutions for diseases. The regulation of cell growth and division is one of the key mechanisms that ensure proper development of living organisms. Compromised regulation of proliferation could lead to cancer, which often starts from epithelial cells. Despite their importance, the exact mechanisms that control proliferation is still under debate. Some believe that mechanical feedback plays the most important role in growth regulation, while others believe that signaling molecules could be responsible for regulation of growth pattern. Computational modeling is used in this study to provide new insights into cellular growth regulation. Up to date, various approaches have been employed to model the proliferation of epithelial cells. There are topological models that emphasize cellular connectivity, lattice-based models that use fixed lattice to represent cells, and off-lattice models that describe cells by collection of connected points. However, existing models are insufficient to capture mechanical properties of the epithelial sheet, partially because of the artificially imposed geometrical constraints, which often restrict cells to be polygon-shaped. Moreover, the mechanical interaction between cells might be over-simplified because of this approximation.  A novel cell-based off-lattice computational model for studying epithelial proliferation is developed in this study. The model provides a flexible representation for cellular geometry, without imposing assumption of polygon cell shape. Epithelial cells appear as polygon-shaped in model simulations as a result of mechanical interaction. Cellular network transitions in model simulations also naturally emerge as a result of cellular interaction, compared with existing models which often include ad hoc assumptions for such transitions. Results in the ESEM simulations match very well with experimental findings, such as overall cell shape polygon class distribution on the epithelial sheet, and the shifting of polygon class during mitosis. It is also worth mentioning that the new model reproduces mitotic rounding behavior in proliferating epithelia, which is commonly observed but never been modeled in other computational models. In addition, this thesis introduces a parallel algorithm that runs on General Purpose Graphical Processing Unit for model implementation, overcoming computational challenges brought by the new model. A complete source code package of the parallel algorithm is provided as a supplement of this thesis for future extension and development of the model.  This work was supported in part by the National Science Foundation grant CBET 1403887.