Mixing or blending two or more fluids of different viscosities is an important and complex issue in the polymer industry. Simulating these types of processes leads to a better understanding of the flow phenomena that take place during mixing. The boundary element method is ideal to simulate mixing flows, because of the large deformations and moving boundary nature of internal batch mixers and extruders. This paper presents a boundary element simulation of the flow of multi-viscous polymer blends inside extruders and internal mixers, In addition, the governing equations, boundary integrals, and their numerical implementation for creeping flows are presented. The simulation is used to predict the mixing quality of polymer blends in realistic mixing processes. A model describing the relationship of drop strain to matrix strain as a function of viscosity ratio is also presented. The now simulation results are in good agreement with analytical and experimental results.