We quantitatively interpret the recently discovered intriguing phenomenon related to resonance Hyper-Raman (HR) scattering. In resonance HR spectra of all-trans-β-carotene (β-carotene) in solution, vibrations of proximate solvent molecules are observed concomitantly with the solute β-carotene HR bands. It has been shown that these solvent bands are subject to marked intensity enhancements by more than 5 orders of magnitude under the presence of β-carotene. We have called this phenomenon the molecular-near field effect. Resonance HR spectra of β-carotene in benzene, deuterated benzene, cyclohexane, and deuterated cyclohexane have been measured precisely for a quantitative analysis of this effect. The assignments of the observed peaks are made by referring to the infrared, Raman, and HR spectra of neat solvents. It has been revealed that infrared active and some Raman active vibrations are active in the HR molecular near-field effect. The observed spectra in the form of difference spectra (between benzene/deuterated benzene and cyclohexane/deuterated cyclohexane) are quantitatively analyzed on the basis of the extended vibronic theory of resonance HR scattering. The theory incorporates the coupling of excited electronic states of β-carotene with the vibrations of a proximate solvent molecule through solute-solvent dipole-dipole and dipole-quadrupole interactions. It is shown that the infrared active modes arise from the dipole-dipole interaction, whereas Raman active modes from the dipole-quadrupole interaction. It is also shown that vibrations that give strongly polarized Raman bands are weak in the HR molecular near-field effect. The observed solvent HR spectra are simulated with the help of quantum chemical calculations for various orientations and distances of a solvent molecule with respect to the solute. The observed spectra are best simulated with random orientations of the solvent molecule at an intermolecular distance of 10 Å.