We have studied analytically the mean pull on shells of real (anisotropic and/or non-isolated) mass concentrations. Using a non-linear scheme, the radial component of the peculiar velocity is averaged over solid angle (V_0) and mass-averaged (V^*_0) for several different generic configurations. Nine Local Supercluster(LS)-like objects and six Great Attractor(GA)-like structures enabled us to compare the corresponding true density parameters, Omega_0, with the estimates for the standard spherical infall model Omega_est (using V_0) and Omega^*_est (via V^*_0). The results for LS-like superclusters are consistent with those derived for GA-like ones. If we focus our attention on the LS-like objects, the accuracy of Omega^*_est is very poor: absolute values of the relative errors greater than 20 per cent are common and they can reach a level of 50-70 per cent. Underestimates of the density parameter are related to superclusters that are spherical within the reference shell at 15 h^-1 Mpc but have an exterior anisotropic tail. The remaining cases (with interior anisotropy and/or companions) lead to overestimates. A clear conclusion is that the spherical infall model is not a good approximation for estimating Omega_0 by means of measurements, V^*_0, in the halo of an LS-like supercluster. In contrast, the accuracy of Omega_est is relatively good, even in extreme situations with either a dominant companion or dipole anisotropy plus companion (all absolute values of the relative errors are less than 20 per cent). Therefore, the peculiar motions when averaged over 4pi sr (V_0) fit a spherical model relatively well. However, the link between our results and the well-known measurements in the Local Supercluster and the Great Attractor (at the corresponding Local Group radius) is not evident. At the end of the paper we present a discussion on the reliability of the standard view that density-velocity data in both structures suggest an open universe. It is remarked that the estimation of the true density enhancement in the Local Supercluster must be improved (by consideration of a full survey and true distances) before one decides on the value of Omega_0.