We report the electronic, elastic, mechanical, optical, and magnetic properties of Rh2MnX (X = Ti, Hf, Sc, Zr, Zn) Heusler alloys performed within density functional theory. The generalized gradient approximation was used for calculations in the context of the Perdew-Burke-Ernzerhof exchange-correlation energy treatment. The computed elastic constants and elastic moduli show that all investigated alloys are mechanically stable and ductile. It has been found that the magnitudes of the theoretical Vickers hardness values of these alloys are in the range of Ti > Sc > Zr > Hf > Zn. Also, a typical metallic behavior is obtained for all alloys after agreement of mechanical, electronic and optical data. On the other side, all alloys show strong ferromagnetic ordering following the magnetic moment (mu(B)) rank of Ti > Zr > Hf > Sc > Zn. Our calculated mu(B) data also agree well with the former theoretical results of Rh2MnX (X = Ti, Hf, Sc, Zr, Zn) Heusler alloys.