  Protostellar discs are mostly modelled as circular structures of gas and dust
orbiting a protostar. However, a number of physical mechanisms, e.g. the
presence of a (sub)stellar companion or initial axial asymmetry, can cause the
gas and dust orbital motion to become eccentric. Theoretical studies have
revealed that, when present, disc eccentricity is expected to occur with
predictable profiles that can be long-lasting and potentially observable in
protostellar systems. We construct an analytical model predicting the typical
features of the kinematics and morphology of eccentric protostellar discs, with
the final goal of characterising the observational appearance of eccentricity
in discs. We validate the model using a numerical simulation of a circumbinary
disc (where the binary makes the disc eccentric). We finally post-process the
simulation with Monte Carlo Radiative Transfer to study how eccentric features
would appear through the "eyes" of ALMA. Besides the motion of the material on
eccentric Keplerian orbits in the disc orbital plane, the most characteristic
eccentric feature emerging from the analytical model is strong vertical motion
with a typical anti-symmetric pattern (with respect to the disc line of
pericentres). A circumbinary disc with a $\approx 40$ au eccentric cavity
($e_{\rm cav}=0.2$), carved by an $a_{\rm bin}=15$ au binary, placed at a
distance $d=130$ pc, is expected to host in its upper emission surface vertical
oscillations up to $v_{z}\sim 400\, {\rm ms}^{-1}$ close to the cavity edge,
i.e. well within ALMA spectral and spatial resolution capabilities. A residual
spiral pattern in the vertical velocity $\Delta v_{z}\sim 150\, {\rm ms}^{-1}$
of the simulation cannot be captured by the theoretical model, we speculate it
to be possibly linked to the presence of a companion in the system.
