  In this paper we construct new exact solutions in Einstein-Gauss-Bonnet and
Lovelock gravity, describing asymptotically flat black strings. The solutions
exist also under the inclusion of a cosmological term in the action, and are
supported by scalar fields with finite energy density, which are linear along
the extended direction and have kinetic terms constructed out from Lovelock
tensors. The divergenceless nature of the Lovelock tensors in the kinetic terms
ensures that the whole theory is second order. For spherically, hyperbolic and
planar symmetric spacetimes on the string, we obtain an effective Wheeler's
polynomial which determines the lapse function up to an algebraic equation. For
the sake of concreteness, we explicitly show the existence of a family of
asymptotically flat black strings in six dimensions, as well as asymptotically
AdS$_{5}\times R$ black string solutions and compute the temperature, mass
density and entropy density. We compute the latter by Wald's formula and show
that it receives a contribution from the non-minimal kinetic coupling of the
matter part, shifting the one-quarter factor coming from the Einstein term, on
top of the usual non areal contribution arising from the quadratic Gauss-Bonnet
term. Finally, for a special value of the couplings of the theory in six
dimensions, we construct strings that contain asymptotically AdS wormholes as
well as rotating solutions on the transverse section. By including more scalars
the strings can be extended to $p$-branes, in arbitrary dimensions.
