Mitotic rounding (MR) during cell division is critical for the robust segregation of chromosomes into daughter cells and is frequently perturbed in cancerous cells. MR has been studied extensively in individual cultured cells, but the physical mechanisms regulating MR in intact tissues are still poorly understood. A cell undergoes mitotic rounding by simultaneously reducing adhesion with its neighbors, increasing actomyosin contraction around the cortex, and increasing the osmotic pressure of the cytoplasm. Whether these changes are purely additive, synergistic or impact separate aspects of MR is not clear. Specific modulation of these processes in dividing cells within a tissue is experimentally challenging, because of off-target effects and the difficulty of targeting only dividing cells. In this study, we analyze MR in epithelial cells by using a newly developed multi-scale, cell-based computational model that is calibrated using experimental observations from a model system of epithelial tissue growth, the Drosophila wing imaginal disc. The model simulations predict that increase in apical surface area of mitotic cells is solely driven by increasing cytoplasmic pressure. MR however is not achieved within biological constraints unless all three properties (cell-cell adhesion, cortical stiffness and pressure) are simultaneously regulated by the cell. The new multi-scale model is computationally implemented using a parallelization algorithm on a cluster of graphic processing units (GPUs) to make simulations of tissues with a large number of cells feasible. The model is extensible to investigate a wide range of cellular phenomena at the tissue scale.