By using ab initio self-consistent field Hartree-Fork methods and atomic clusters expanding theory and employing Gamess program, two- and three-body interaction energies and the equation of state for solid argon in fcc crystal have been quantificationally calculated at the neighboring atomic distance R=2.40 -4.00 Å under high pressure. In addition, the convergence and truncation of atomic energy multi-body expansion are analyzed. It is found that two-body contribution to the cohesive energy is positive, while the three-body contribution is negative in solid argon under high pressure. At high pressure, only the consideration of the two-body contribution will overestimate the cohesive energy, hence it is necessary to introduce the three-body negative effects. The phenomenon of the experiment under 80GPa can be explained by considering the three-body potential.