The study of the structural, electronic, thermodynamic, elastic and magnetic properties of rare‐earth based full Heusler alloys Mn2LuZ (Z = B, Al, Ga and In) have been carried out using the full‐potential linearized muffin‐tin orbital method (FP‐LMTO), within density functional theory (DFT) and generalized gradient approximation (GGA) for exchange and correlation energy. The electronic properties studied have shown that the compounds have a metallic behavior. We have also computed the mechanical properties where we found these full Heusler compounds are mechanically stable. Using the quasi‐harmonic Debye model, the variations of bulk modulus, thermal expansion coefficient, heat capacities, Debye temperature and Gibbs free energy with pressures covering the 0–40 GPa interval and temperatures ranging from 0 to 1500 K were also investigated and in‐depth discussed. The calculated properties represent a solid prediction for the Mn2LuZ (Z = B, Al, Ga and In) Heusler compounds and are awaiting for experimental concretization.