The production cross sections of 10Be and 26Al were measured by accelerator mass spectrometry using 89Y, 159Tb, and natCu targets bombarded by protons with energies Ep of 120 GeV and 392 MeV. The production cross sections obtained for 10Be and 26Al were compared with those previously reported using Ep = 50 MeV-24 GeV and various targets. It was found that the production cross sections of 10Be monotonically increased with increasing target mass number when the proton energy was greater than a few GeV. On the other hand, it was also found that the production cross sections of 10Be decreased as the target mass number increased from that of carbon to those near the mass numbers of nickel and zinc when the proton energy was below approximately 1 GeV. They also increased as the target mass number increased from near those of nickel and zinc to that of bismuth, in the same proton energy range. Similar results were observed in the production cross sections of 26Al, though the absolute values were quite different between 10Be and 26Al. The difference between these production cross sections may depend on the impact parameter (nuclear radius) and/or the target nucleus stiffness.