The material properties of heterogeneous polymer blends are crucially influenced by their morphology, i.e., by the spatial Structure of the blend components and by the Specific configuration of the interfaces separating the phases. Hence. in order to understand the behavior of experimentally obtained morphologies. one is interested in modeling the relevant dynamics of the morphology subject to external flow. Thus one can Study. e.g.. through the interfacial stress tensor the rheological properties due to the interfaces. The balance equations used for that purpose are based on a Cahn-Hilliard equation for the local concentration. the continuity equation. and a modified Navier-Stokes equation for the local velocity. The essential material and processing parameters such as surface tension, viscosity and volume fraction of both polymers. and imposed shear rate are taken into consideration as model coefficients. By regarding hydrodynamic interaction, which is proved to be important in case or immiscible blends, the interfacial relaxation is described properly. Simulations in both three and two dimensions agree at least qualitatively with experimental results concerning droplet deformation. droplet coalescence, and interfacial rheological properties of the blend.