  In this paper measurements are presented of $\rm \pi$$^+$, $\rm \pi$$^-$,
K$^+$, K$^-$, p and $\overline{\rm p}$ production at mid-rapidity < 0.5, in
Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV as a function of centrality.
The measurement covers the transverse momentum ($p_{\rm T}$) range from 100,
200, 300 MeV/$c$ up to 3, 3, 4.6 GeV/$c$, for $\rm\pi$, K, and p respectively.
The measured $p_{\rm T}$ distributions and yields are compared to expectations
based on hydrodynamic, thermal and recombination models. The spectral shapes of
central collisions show a stronger radial flow than measured at lower energies,
which can be described in hydrodynamic models. In peripheral collisions, the
$p_{\rm T}$ distributions are not well reproduced by hydrodynamic models.
Ratios of integrated particle yields are found to be nearly independent of
centrality. The yield of protons normalized to pions is a factor ~1.5 lower
than the expectation from thermal models.
