The elliptic, v2, triangular, v3, and quadrangular, v4, azimuthal anisotropic flow coefficients are measured for unidentified charged particles, pions, and (anti-)protons in Pb-Pb collisions at sNN=2.76TeV with the ALICE detector at the Large Hadron Collider. Results obtained with the event plane and four-particle cumulant methods are reported for the pseudo-rapidity range |η|<0.8 at different collision centralities and as a function of transverse momentum, pT, out to pT=20GeV/c. The observed non-zero elliptic and triangular flow depends only weakly on transverse momentum for pT>8GeV/c. The small pT dependence of the difference between elliptic flow results obtained from the event plane and four-particle cumulant methods suggests a common origin of flow fluctuations up to pT=8GeV/c. The magnitude of the (anti-)proton elliptic and triangular flow is larger than that of pions out to at least pT=8GeV/c indicating that the particle type dependence persists out to high pT. © 2013 CERN.