The flow instability in a flow front during the injection stage of injection molding process was theoretically investigated for polymeric materials. In addition, the relationship between the flow instability and flow mark on the surface of injection moldings was also examined. According to the theory, the flow in the front region becomes unstable when the shear stress exceeds the normal stress. Whether flow marks occur or not is also controlled by the balance between the normal and shear stresses in the region. The validity of this criterion was verified experimentally for the injection moldings of polypropylene (PP)/rubber/talc blends. The surface appearance for the moldings was more excellent for the blends with lower critical shear rates where the shear stress becomes equal to the normal stress; namely, the enhancement of the elasticity of polymer melts at low shear rates effectively prevents the occurrence of the flow marks for the injection moldings.