  We study Kundt solutions of topologically massive gravity (TMG) and the new
theory of massive gravity (NMG), proposed recently in arXiv:0901.1766. For
topologically massive gravity, only the CSI Kundt solutions (i.e., solutions
with constant scalar polynomial curvature invariants) were found very recently
in arXiv:0906.3559. We find non-CSI explicit solutions of TMG, when
$\Lambda=-\mu^2$, and these are the first such solutions. For the new theory of
massive gravity, after reducing the field equations to a manageable system of
differential equations, the CSI solutions are discussed in detail, with a focus
on a subfamily whose solutions are particulary easy to describe. A number of
properties of Kundt solutions of TMG and NMG, such as an identification of
solutions which lie at the intersection of the full non-linear and linearized
theories, are also derived.
