Reactions of protons induced on 208Pb and 209Bi, the important target materials in accelerator- driven systems, are studied. First, a set of proton optical model potential parameters for heavy elements is obtained up to 500 MeV. Theoretical total reaction cross sections and elastic scattering angular distributions determined by this set of optical model parameters reproduce the experimental data well. Second, several nuclear reaction models (optical model, intranuclear cascade mechanism for nucleon emission, preequilibrium theory based on the exciton model, evaporation model, and the direct reaction theory) are extended for medium energy, and the various reactions of p + 208Pb and 209Bi are calculated in the energy region from threshold up to 250 MeV. In particular, the inclusive cross sections of six emission particles and the production cross sections of all residual nuclei, as well as their energy spectra, are calculated and discussed.