The transverse momentum (pT) spectra and elliptic flow coefficient (v2) of deuterons and anti-deuterons at mid-rapidity (| y| < 0.5) are measured with the ALICE detector at the LHC in Pb–Pb collisions at sNN = 2.76 TeV. The measurement of the pTspectra of (anti-)deuterons is done up to 8 GeV/ c in 0–10% centrality class and up to 6 GeV/ c in 10–20% and 20–40% centrality classes. The v2is measured in the 0.8 < pT<5 GeV/ c interval and in six different centrality intervals (0–5, 5–10, 10–20, 20–30, 30–40 and 40–50%) using the scalar product technique. Measured π±, K± and p+p ¯ transverse-momentum spectra and v2are used to predict the deuteron pTspectra and v2within the Blast-Wave model. The predictions are able to reproduce the v2 coefficient in the measured pTrange and the transverse-momentum spectra for pT> 1.8 GeV/ c within the experimental uncertainties. The measurement of the coalescence parameter B2is performed, showing a pT dependence in contrast with the simplest coalescence model, which fails to reproduce also the measured v2 coefficient. In addition, the coalescence parameter B2 and the elliptic flow coefficient in the 20–40% centrality interval are compared with the AMPT model which is able, in its version without string melting, to reproduce the measured v2(pT) and the B2(pT) trend.