On the basis of the generalized van der Waals equations of state, the quasispinodal and the supercritical-point parameters of the Generation IV nuclear reactor coolant materials, namely, sodium, lead and bismuth, have been determined. To improve accuracy, the known van der Waals equation of state has been generalized in three different ways. That is, the attractive term in the van der Waals equation of state has been modified by introducing new substance-specific parameters. The parameters of the generalized van der Waals equations of state have been determined through vapor-liquid critical-point parameters. The mean percentage error in the determined quasispinodal for sodium, lead, and bismuth is less than 3% in comparison with the Semenchenko correlation. T he temperature correlation of the quasispinodal pressure for sodium, lead, and bismuth, formulated in this work, is statistically excellent with the mean correlation coefficient of 0.99995 and the coefficient of determination of 0.999895. The mean supercritical-point parameters of sodium, lead, and bismuth, based on the three-parameter generalized van der Waals equations of state, are found to be (28.80 MPa, 15.1563 10−5 m3/mol, and 2563 K), (207.2275 MPa, 8.876 10−5 m3/mol, and 5278 K) and (155.338 MPa, 10.5923 10−5 m3/mol, and 4788 K) respectively. The generalized van der Waals equations of state are presented in the reduced form from which follows the law of corresponding states.