A hydrodynamic homogeneous model has been developed for the motion of mutually impenetrable viscoelastic non-Newtonian fluids taking into account surface tension forces. Based on this model, numerical simulations of cytokinesis hydrodynamics were performed. The cytoplasm is considered a non-Newtonian viscoelastic fluid. The model allows for the calculation of the formation and rupture of the intercellular bridge. Results from an analytical analysis shed light on the influence of the viscoelastic fluid’s relaxation time on cytokinesis dynamics. A comparison of numerical simulation results and experimental data showed satisfactory agreement.