  We study the gamma-ray burst GRB 081008 environment by analysing the spectra
of its optical afterglow. UVES high resolution spectroscopy of GRB 081008 was
secured ~5 hr after the Swift trigger. Our dataset comprises also three FORS2
nearly simultaneous spectra of the same source. The availability of nearly
simultaneous high and low resolution spectra for a GRB afterglow is an
extremely rare event. The GRB-Damped Lyman Alpha system at z = 1.9683 shows
that the interstellar medium (ISM) of the host galaxy is constituted by at
least three components which contribute to the line profiles. Component I is
the redmost one, and is 20 km/s and 78 km/s redward component II and III,
respectively. We detect several ground state and excited absorption features in
components I and II. These features have been used to compute the distances
between the GRB and the absorbers. Component I is found to be 52 +/- 6 pc away
from the GRB, while component II presents few excited transitions and its
distance is 200+60-80} pc. The hydrogen column density associated to GRB 081008
is log NH/cm^-2 = 21.11 +/- 0.10, and the metallicity of the host galaxy is in
the range [X/H] = -1.29 to -0.52. In particular, we found [Fe/H]=-1.19 +/- 0.11
and [Zn/H]=-0.52 +/- 0.11 with respect to solar values. This discrepancy can be
explained by the presence of dust in the GRB ISM, given the opposite refractory
properties of iron and zinc. By deriving the depletion pattern for GRB 081008,
we find the optical extinction in the visual band to be AV ~ 0.19 mag. The
Curve of Growth analysis applied to the FORS2 spectra brings column densities
consistent at the 3 sigma level to that evaluated from the UVES data using the
line fitting procedure. This reflects the low saturation of the detected
GRB\,081008 absorption features.
