Stopping cross sections of α particles for 12 solid elements Se, Y, Zr, Nb, Mo, Sb, Te, La, Dy, Ta, W, and Au have been measured for 0.3<=Eα<=2.0 MeV. Structure additional to that previously obtained was observed, in the periodic dependence of the stopping cross section on the atomic number of the stopping element. Good agreement in the periodic dependence of the structure was found when the experimental results were compared to theoretical calculations based on Lindhard's statistical approach, carried out by Rousseau, Chu, and Powers. The energy dependence of the stopping cross section was examined by fitting the experimental results to a three-parameter formula recently suggested by Brice. The usefulness of this formula in extrapolating the results to energy regions outside the measurements is investigated.