The study of the processes and mechanisms of the medium group mass nuclear systems formation (formed in reactions with protons) has both an important fundamental and practical significance. These tasks are especially important for the production of medical radionuclides, which are used for the effective early diagnosis and treatment of the various cancers. Combining the methods of radionuclide imaging with the methods of radionuclide therapy (therapy plus diagnostics—theranostics), it is possible to implement unique methods of non-surgical treatment of tumors with their precise visualization and minimal side effects. Therefore, in this work the experimental and theoretical studies of the nuclear reaction excitation functions with targets: 117Sn and 119Sn in the proton energy range of 6–18 MeV are carried out. Cross sections of the formation of antimony radionuclides are obtained for these reactions, and the mechanisms of such reactions are analyzed. Antimony radionuclides are promising for use in theranostics.