  In this paper we study black string solutions under the consideration of
rainbow gravity. We have analytically obtained the solution for
four-dimensional black strings in terms of the functions $f(E/E_p)$ and
$g(E/E_p)$ that sets the energy scale where the rainbow gravity becomes
relevant. We have also obtained the Hawking temperature for the black string,
from which we could see that the rainbow functions play the role of increasing
or decreasing the Hawking temperature for a given horizon radius depending on
the choice of such rainbow functions. We have computed the entropy, specific
heat and free energy for the black string. The entropy and specific heat
exhibit a rainbow dependence, while the free energy is not modified by the
rainbow functions. Finally we have studied the effects of the rainbow gravity
in the orbits of massive and massless particles around a black string. We could
verify that neither massive nor massless particles exhibit stable orbits around
a black string in the scenario of rainbow gravity, for any configuration of
rainbow functions.
