The collision-induced hyper-Rayleigh (CIHR) spectra of the gaseous H(2)-Ar mixture are discussed in the binary regime on the basis of our ab initio computed H(2)-Ar collision-induced (CI) first dipole hyperpolarizability tensor Deltabeta(R). A method for the computation of the spherical, rotationally adapted components Deltabeta(lambdaL) ((s,K))(R) of Deltabeta(R) needed for spectroscopic line shape analysis is proposed. Both the vector and the septor parts of the H(2)-Ar CIHR spectrum are evaluated at room (T=295 K) temperature. The spectra are calculated assuming the full quantum computations based on the Schrodinger equation of the relative translational motion of H(2)-Ar as well as semiclassical methods (classical trajectory approach and Birnbaum-Cohen model translational profiles). The H(2)-Ar pair CIHR septor spectrum has been found stronger than the vector one.