In this paper measurements are presented of pion±, K±, p, and p ̄ production at midrapidity (|y| < 0.5), in Pb-Pb collisions at √sNN = 2.76 TeV as a function of centrality. The measurement covers the transverse-momentum (pT ) range from 100, 200, and 300 MeV/c up to 3, 3, and 4.6 GeV/c for pion, K, and p, respectively. The measured pT 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, whichcanbedescribedinhydrodynamicmodels.Inperipheralcollisions,thepT distributionsarenotwellrepro- duced 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.