Abstarct: We have calculated pressure, internal energy, and infinite-frequency shear modulus of two-body Hartree-Fock dispersion (HFD)-like and Lennard-Jones (LJ) potentials using the statistical mechanical formula for argon and neon, respectively. The required radial distribution functions (RDFs) have been used from two recently determined accurate exxpressions in the literature. Molecular dynamics simulations have been also applied to generate an exxpression for the RDF of HFD-like fluid in the range 0.5 ≤ T*≤ 5.1 and 0.35 ≤ ρ*≤ 1.1. Quantum corrections for the LJ system have been considered using the Feynman–Hibbs (FH) and Wigner- Kirkwood (WK) approaches. To take many-body forces into account for the HFD-like system, the simple three-body potentials of Guzman et al. (2011), Wang and Sadus (2006), and Hauschild and Prausnitz (1993) used with the two-body potential without requiring an expensive three-body calculation. The results show that the quantum and three-body effects improve the prediction of the pressure and internal energy of the HFD-like and LJ fluids.