We study the mass distribution in six nearby ( z < 0.06 ) relaxed Abell clusters of galaxies A0262 , A0496 , A1060 , A2199 , A3158 and A3558 . Given the dominance of dark matter in galaxy clusters we approximate their total density distribution by the NFW formula characterized by virial mass and concentration . We also assume that the anisotropy of galactic orbits is reasonably well described by a constant and that galaxy distribution traces that of the total density . Using the velocity and position data for 120-420 galaxies per cluster we calculate , after removal of interlopers , the profiles of the lowest-order even velocity moments , dispersion and kurtosis . We then reproduce the velocity moments by jointly fitting the moments to the solutions of the Jeans equations . Including the kurtosis in the analysis allows us to break the degeneracy between the mass distribution and anisotropy and constrain the anisotropy as well as the virial mass and concentration . The method is tested in detail on mock data extracted from N -body simulations of dark matter haloes . We find that the best-fitting galactic orbits are remarkably close to isotropic in most clusters . Using the fitted pairs of mass and concentration parameters for the six clusters we conclude that the trend of decreasing concentration for higher masses found in cosmological N -body simulations is consistent with the data . By scaling the individual cluster data by mass we combine them to create a composite cluster with 1465 galaxies and perform a similar analysis on such sample . The estimated concentration parameter then lies in the range 1.5 < c < 14 and the anisotropy parameter in the range -1.1 < \beta < 0.5 at the 95 percent confidence level .