AbstractStructure‐property relations for the encapsulated FENE dumbbell correlate well with experimental observations for concentrated polymer solutions. Relying on rigorous kinetic theory results, we derive an expression for the polymeric mass flux relative to the mass‐average velocity (diffusive flux). The form of this flux implies non‐Fickian diffusion with its own intrinsic time scale. For steady flow in an infinitely long tube nonuniform concentration profiles are predicted.