  Aim: We aim to compute the mass and velocity anisotropy profiles of Abell
2142 and, from there, the pseudo phase--space density profile $Q(r)$ and the
density slope - velocity anisotropy $\beta - \gamma$ relation, and then to
compare them with theoretical expectations. Methods: The mass profiles were
obtained by using three techniques based on member galaxy kinematics, namely
the caustic method, the method of Dispersion - Kurtosis, and MAMPOSSt. Through
the inversion of the Jeans equation, it was possible to compute the velocity
anisotropy profiles. Results: The mass profiles, as well as the virial values
of mass and radius, computed with the different techniques agree with one
another and with the estimates coming from X-ray and weak lensing studies. A
concordance mass profile is obtained by averaging the lensing, X-ray, and
kinematics determinations. The cluster mass profile is well fitted by an NFW
profile with $c=4.0 \pm 0.5$. The population of red and blue galaxies appear to
have a different velocity anisotropy configuration, since red galaxies are
almost isotropic, while blue galaxies are radially anisotropic, with a weak
dependence on radius. The $Q(r)$ profile for the red galaxy population agrees
with the theoretical results found in cosmological simulations, suggesting that
any bias, relative to the dark matter particles, in velocity dispersion of the
red component is independent of radius. The $\beta - \gamma$ relation for red
galaxies matches the theoretical relation only in the inner region. The
deviations might be due to the use of galaxies as tracers of the gravitational
potential, unlike the non--collisional tracer used in the theoretical relation.
