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In this paper, we study the scalar (tensor) and vector unparticle corrections for cosmic and black strings. Initially, we consider a static cosmic string ansatz from which we obtain the solution in terms of first- and second-kind Bessel functions. We also obtain the solution for a black string in the unparticle scenario. We identify two regimes, namely, a gravity-dominated regime and an ungravity-dominated regime. In the gravity-dominated regime, the black string solution recovers the usual solution for black strings. The Hawking temperature is also studied in both regimes. As in the static and rotating black hole, we find a fractalization of the event horizon. This points to the fact that fractalization is a natural consequence of unparticles. Finally, we study the thermodynamics of the black string in the ungravity scenario by computing the entropy, heat capacity, and free energy. For both cases, we find that, depending on the region of the parameter d U , phase transitions are possible. [ABSTRACT FROM AUTHOR]