Heusler alloys are a huge family of binary, ternary and quaternary compounds and contain a wide range of unique properties, which made Heusler compounds to be the efficient materials for diverse applications. When it comes to the commercial applications mechanical properties are worth of check on and turn out to be the significant factor in the processing and final use of the materials. These properties make the study proficient by examine the nature of material under external pressure. In this study, we estimated mechanical properties of Rh2MnZn full-Heusler alloy using the full-potential linearized augmented plane wave method (FP-LAPW) method within the density functional theory (DFT). We have obtained C11, C12 and C44 elastic constants due to cubic symmetry using Charpin method implemented in Wien2k code. Further, using these elastic constants mechanical properties such as bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, anisotropic factor and Cauchy’s pressure are calculated. These moduli depicted hardness, ductility and elastic anisotropy of the alloy.