  We examine a class of cylindrically symmetric solutions in Horava-Lifshitz
gravity. For the relativistic value of the coupling constant, $ \lambda=1 $, we
find the "hedgehog" type static black string solution with the nonvanishing
radial shift in the ADM-type decomposition of the spacetime metric. With zero
radial shift, this solution corresponds to the usual BTZ black string in
general relativity. However, unlike the general relativity case, the BTZ type
black strings do naturally exist in HL gravity, without the need for any
specific source term. We also find a rotating BTZ type black string solution
which requires the nonvanishing radial shift for its very existence. We
calculate the mass and the angular momentum of this solution, using the
canonical Hamiltonian approach. Next, we discuss the Lemos type black string,
which is inherent in general relativity with a negative cosmological constant,
and present the static metric for any value of $ \lambda > 1/3 $. Finally, we
show that while, for $\lambda=1 $, the entropy of the Lemos type black string
is given by one quarter of the horizon area, the entropy of the static BTZ type
black string is one half of its horizon area.
