We propose generalized geometrical scaling for elastic hadron-hadron scattering which has the scaling dimensional parameter [radical][sigma][sub [ital t]]/[kappa]([ital x]) , [kappa]([ital x]) being a function of the elasticity [ital x] characteristic of the form of the eikonal. This hypothesis presents a unified explanation of the features of the differential cross sections of [ital pp] and [ital [bar p]p] scattering in the energy region from the CERN Intersecting Storage Ring to the Fermilab Tevatron collider with the eikonal corresponding to the dipole-type form factor.