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Caesium-137 (Cs-137) is a harmful and toxic radioisotope emitting beta rays dan gamma rays with a relatively long half-life of 30.17 years. Caesium-137 radioisotope can be found in nuclear waste as a fission product in nuclear reactors or nuclear fallouts. In this work, transmutation of Cs-137 nuclear waste was theoretically studied by a 13-MeV proton bombardment. The TALYS 1.95 code was employed to calculate nuclear cross-sections of (p,n), (p,2n), (p,np), (p,2p), p,d), (p,t), (p,He-3) and (p,α) in the proton energy range between 0 and 20 MeV. From the TALYS calculated nuclear cross-sections for 13-MeV protons, it was revealed that only two nuclear reactions were significant, i. e. (p,n) and (p,2n), whereas the other nuclear reactions had cross-sections of much lower than 1 mbarn which might result in undetectably low radioactivity. From the two significant nuclear reactions, two stable isotopes, i. e. Ba-137 and Ba-136 could be produced via 137Cs(p,n)137Ba and 137Cs(p,2n)136Ba nuclear reactions. The calculated transmutation yields at a 13 MeV proton bombardment for 137Cs(p,n)137Ba and 137Cs(p,2n)136Ba nuclear reactions were 7.05x104 atoms/µAs and 1.89x105 atoms/µAs, respectively. This theoretical study highlights that a medium energy proton beam can possibly be used to transmute Cs-137 nuclear waste to stable isotopes. [ABSTRACT FROM AUTHOR]