The absolute differential cross sections for elastic scattering of 31-Mev He3 ions on Be, Al, Cu, Sn(nat), Sn120, and Bi have been measured in the angular range of approximately 10 to 120 deg in the center-of-mass system. Thin self-supporting foil targets were chosen to span the parameter A 1/3, where A is the target mass number. The first excited states of the isotopes of the above elements had sufficient energy separation from the ground state to enable elastic scattering to be resolved from inelastic scattering. The detection system, consisting of Cal(Tl) scintillation crystals, was capable of 3%pulse-height resolution and 1 degree angular resolution. Characteristically, the light-element angular distributions show strong diffraction effects. The differential cross section divided by the Rutherford cross section decreases exponentially at large angles for the heavy elements, and the differential cross sections break away from Rutherford behavior at angles which increase almost linearly with increase of atomic number of the target nucleus. A comparison of the results for natural tin, and tin enriched to 85% in Sn120, indicated that within the experimental uncertainties over the measured angular interval, there were no pronounced isotopic effects. The data are presented both in tabular and graphical form to allow …