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.