Steinberg-Cochran-Guinan (SCG) model, the corrected SCG model and the finite strain theory were reviewed with respect to the basic assumptions and applicability, and the shear modulus data of aluminum under shock compression predicted by these models were compared with the available data obtained in one-dimensional plate impact experiments. The comparison shows that the corrected SCG model is the best one,being capable of describing the variation of the measured shear modulus of aluminum with shock pressure, although the other two are applicable at lower pressure. It is found that the shear modulus increases gradually with the increase of shock pressure in the range of 10—80GPa due to the work-hardening effects. As the shock pressure goes above ～80GPa, the shear modulus of aluminum falls quickly due to the dominating effect of high-temperature softening, and when the shock pressure reaches ～125GPa， corresponding to the onset of melting on Hugoniot, the shear modulus of aluminum decreases to zero.