  We study the effect of non-radial motions on the mass function, the velocity
dispersion function (hereafter VDF) and on the shape of clusters of galaxies
using the model introduced in Del Popolo & Gambera (1998a,b; 1999). The mass
function of clusters, obtained using the quoted model, is compared with the
statistical data by Bahcall & Cen (1992a,b) and Girardi et al. (1998), while
the VDF is compared with the Center for Astrophysics (hereafter CfA) data by
Zabludoff et al. (1993) for local clusters and those of Mazure et al. (1996)
and Fadda et al. (1996). In both cases the model predictions are in good
agreement with the observational data showing once more how non-radial motions
can reduce many of the discrepancies between Cold Dark Matter (hereafter CDM)
model predictions and observational data. Finally we study the effect of
non-radial motions on the intrinsic shape of clusters of galaxies showing that
non-radial motions produce clusters less elongated with respect to CDM model in
agreement with de Theije et al. (1995, 1997) results.
