The production of the prompt charmed mesons D0, D+, and D*+ relative to the reaction plane was measured in Pb-Pb collisions at a center-of-mass energy per nucleon-nucleon collision of √sNN=2.76TeV with the ALICE detector at the CERN Large Hadron Collider. D mesons were reconstructed via their hadronic decays at central rapidity in the transverse-momentum (pT) interval 2–16 GeV/c. The azimuthal anisotropy is quantified in terms of the second coefficient v2 in a Fourier expansion of the D-meson azimuthal distribution and in terms of the nuclear modification factor RAA, measured in the direction of the reaction plane and orthogonal to it. The v2 coefficient was measured with three different methods and in three centrality classes in the interval 0%–50%. A positive v2 is observed in midcentral collisions (30%–50% centrality class), with a mean value of 0.204+0.099−0.036 (tot. unc.) in the interval 2