  The transverse momentum ($p_{\rm T}$) spectra and elliptic flow coefficient
($v_2$) 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
$\sqrt{s_{\rm NN}} = 2.76$ TeV. The measurement of the $p_{\rm T}$ spectra of
(anti-)deuterons is done up to 8 GeV/$c$ in 0-10% centrality class and up to
GeV/$c$ in 10-20% and 20-40% centrality classes. The $v_2$ is measured in the
$0.8 <p_{\rm T} <5$ 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 $\pi^{\pm}$, K$^{\pm}$ and p+$\overline{\mathrm{p}}$
transverse-momentum spectra and $v_2$ are used to predict the deuteron $p_{\rm
T}$ spectra and $v_2$ within the Blast-Wave model. The predictions are able to
reproduce the $v_2$ coefficient in the measured $p_{\rm T}$ range and the
transverse-momentum spectra for $p_{\rm T}>1.8$ GeV/$c$ within the experimental
uncertainties. The measurement of the coalescence parameter $B_2$ is performed,
showing a $p_{\rm T}$ dependence in contrast with the simplest coalescence
model, which fails to reproduce also the measured $v_2$ coefficient. In
addition, the coalescence parameter $B_2$ 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 $v_2$($p_{\rm
T}$) and the $B_2$($p_{\rm T}$) trend.
