  We compute the next-to-next-to-leading order QCD corrections to the graviton
production in models of TeV-scale gravity, within the soft-virtual
approximation.
  For the Arkani-Hamed, Dimopoulos and Dvali (ADD) model we evaluate the
contribution to the Drell-Yan cross section, and we present distributions for
the di-lepton invariant mass at the LHC with a center-of-mass energy
$\sqrt{s_H}=14\text{TeV}$. We find a large $K$ factor ($K\simeq 1.8$) for large
values of invariant mass, which is the region where the ADD graviton
contribution dominates the cross section. The increase in the cross section
with respect to the previous order result is larger than $10\%$ in the same
invariant mass region. We also observe a substantial reduction in the scale
uncertainty.
  For the Randall-Sundrum (RS) model we computed the total single graviton
production cross section at the LHC. We find an increase between $10\%$ and
$13\%$ with respect to the next-to-leading order prediction, depending on the
model parameters. We provide an analytic expression for the NNLO $K$ factor as
a function of the lightest RS graviton mass.
