  The precision of the Gaia data offers a unique opportunity to study the
internal velocity field of star clusters. We develop and validate a
forward-modelling method for the internal motions of stars in a cluster. The
model allows an anisotropic velocity dispersion matrix and linear velocity
gradient describing rotation and shear, combines radial velocities available
for a subset of stars, and accounts for contamination from background sources
via a mixture model. We apply the method to Gaia DR2 data of the Hyades cluster
and its tidal tails, dividing and comparing the kinematics of stars within and
beyond 10 pc, which is roughly the tidal radius of the cluster. While the
velocity dispersion for the cluster is nearly isotropic, the velocity ellipsoid
for the tails is clearly elongated with the major axis pointing towards the
Galactic centre. We find positive and negative expansion at $\approx 2\sigma$
significance in Galactic azimuthal and vertical direction for the cluster but
no rotation. The tidal tails are stretching in a direction tilted from the
Galactic centre while equally contracting as the cluster in Galactic vertical
direction. The tails have a shear (A) of $16.90\pm 0.92$ m/s/pc and a vorticity
(B) of $-6.48\pm1.15$ m/s/pc, values distinct from the local Oort constants.
