The aim of this paper is to calculate the analytical form of the equation of state until the third virial coefficient of a classical system interacting via an effective potential of fully Ionized Plasmas. The excess osmotic pressure is represented in the forms of a convergent series expansions in terms of the plasma Parameter $\mu _{ab} = {{{e_a e_b \chi } \over {DKT}}}$μab=eaebχDKT, where χ2 is the square of the inverse Debye radius. We consider only the thermal equilibrium plasma.