  In this paper, we study the various cylindrical solutions (cosmic strings) in
gravity's rainbow scenario. In particular, we calculate the gravitational field
equations corresponding to energy-dependent background. Further, we discuss the
possible Kasner, quasi-Kasner and non-Kasner exact solutions of the field
equations. In this framework, we find that quasi-Kasner solutions can not be
realized in gravity's rainbow. Assuming only time-dependent metric functions,
we also analyse the time-dependent vacuum cosmic strings in gravity's rainbow,
which are completely different than the other GR solutions.
