The Raman spectra of the vibrational fundamental, first overtone and second overtone transitions of the H2 molecule were recorded using visible and ultraviolet argon–ion laser excitation. The ratios of transition polarizability matrix elements, α01,21/α01,11 and α01,31/α01,11, were determined from the measured intensities of the Q(1) Raman lines v,J=0,1→v′,1 for v′=1,2,3. The experimentally determined value of the Raman first overtone matrix element is in good agreement with the value from the best ab initio calculation.