Intracellular flow of cytoplasmic fluid during cell cytokinesis is investigated. The intercellular bridge connecting two daughter cells is modeled as a cylindrical microchannel whose squeezing causes cytoplasmic flow inside the bridge itself and into the daughter cells. An equation from recent experimental measurements by Zhang and Robinson [W. Zhang, D.N. Robinson, Balance of actively generated contractile and resistive forces controls cytokinesis dynamics, Proceedings of the National Academy of Sciences of the United States of America 102 (2005) 7186-7191.] that governs the dynamics of bridge thinning is implemented in this model. The purpose of this research is to compute intracellular flow induced by the bridge thinning process. Two different types of boundary conditions are compared at the membrane-cytoplasm interface; these are a no-slip condition and a no tangential stress condition. Pressure and flow velocity distributions in the daughter cells and the force exerted by this flow on the daughter cell nucleus are computed. It is established that the pressure difference between the daughter cell and the intercellular bridge increases as time progresses. It is also observed that a region of stagnation develops on the downstream side of the nucleus as the bridge thins.