The stopping powers of Ta and Mo were measured respectively for protons of 4.5-20.0 MeV and 4.0-12.5 MeV, with an accuracy of ±0.3%. The results for Mo agree very well with the calculated values in ICRU Report 49. By analyzing the experimental results using the modified Bethe-Bloch formula including the Barkas correction, we deduced the mean excitation energy, the I value. In this analysis, we used the Barkas correction of Ashley, Ritchie and Brandt and Bonderup's and Bichsel's shell corrections for the shell correction. The I values, respectively obtained with the Bonderup and Bichsel shell corrections, were 685.1 ± 30.2 eV and 743.1 ± 24.8 eV for Ta and 420.3 ± 14.8 eV and 426.9 ± 13.4 eV for Mo. These two I values for Ta differ and the Bonderup shell correction does not fit the experimental data well. On the other hand, the I values for Mo are very similar and the Bonderup and Bichsel shell corrections both reproduce the experimental situation nearly equally well.