Hexagonal-structured high-entropy alloys (HEAs) are in use for engineering materials, for critical components in chemical processing, power generation and gas turbine. The present work described how HEAs behave regarding their thermophysical properties and their exceptional elastic and mechanical properties. In the beginning, higher-order elastic constants (HOECs) of the HEAs, namely Cr10Mn30Fe50Co10, Cr20Mn20Fe34Co20Ni6, Cr20Mn20Fe30Co20Ni10, Cr20Mn20Fe20Co20Ni20 and Cr25Fe25Co25Ni25, in their hcp phase have been computed with the help of simple interaction potential approach. Utilizing HOECs, the elastic moduli, anisotropy factor (fE), Pugh’s ratio (B/G), Kleinman’s parameter (ζ), Poisson’s ratio (σ), microhardness (H), Vicker’s hardness (HV), Lame’s constants (λ and µ) and ratio of linear compressibility coefficients (f) have been computed. Later on, the Grüneisen parameter for the shear wave and longitudinal wave of considered HEAs has been calculated utilizing the obtained values of HOECs and lattice parameters. The results of second-order elastic constants were compared with the results obtained from different theories. The obtained results may be further explored for determining the inherent properties of HEAs.