Polyethylene (PE) or polycarbonate (PC) drop deformation and the breakup mechanism in a PE melt under shear flow were investigated using numerical simulations. The volume of fluid (VOF) method in FIDAP was used to track the dynamic interface. Two models were built for the investigation of a PE/PE system and a PE/PC system. Experimental data of polymer properties, such as specific heat capacity, viscosity, and heat conductivity, were incorporated in the simulations. For the PE/PE system, a temperature-dependent viscosity model was used for the matrix PE and the dispersed PE. For the PE/PC system, generalized viscosity models were used for PE and PC with time-dependent moving boundaries. An erosion mechanism similar to that observed in previous experiments was found for deformation and breakup of both PE and PC in the PE melt under simple shear flow. Local flow information, such as temperature, shear rate, viscosity, and shear stress, was obtained from the simulation results. The shear stress at the interface was much higher than the shear stress either in the dispersed phase or in the matrix phase, which could explain the erosion breakup mechanism.