To theoretically analyze the mechanical behaviors of rheological rate effect, the rheological model of unsaturated soil should be formulated. First, the yield surfaces of unsaturated soil are divided into LC and SI yield surfaces. Second, based on the compression creep formula of the LC yield surface, the corresponding rate of viscoplastic volumetric strain is formulated by the equivalent-time method.Combined with Barcelona yield equation and the associated flow law, the three-dimensional rheological rate equation of the LC yield surface is obtained.Differences and similarities between the LC subsequent yield equation of Gennaro-Pereira are discussed. Then, based on the suction-induced compression creep formula of SI yield surface,the corresponding viscoplatic volumetric strain rate is formulated by the equivalent-time method. Finally, the equivalent-time three-dimensional elastic viscoplastic model of unsaturated soil is built combining the rheological rate equations of LC and SI yield surfaces with elastic equation.When the rheological rate effect is ignored, LC and SI rheological yield equations can be degenerated into the corresponding plastic yield equations of Barcelona model. One-dimensional rheological behaviors are theoretically analyzed,and the theoretical predicts and the soil test data are in relatively good agreement. The numerical analysis results of rheological behaviors under three-axial loading condition show that when the same dead loading is applied by several ways, along with the duration of dead loading, the rheological volumetric strains at different ways will tend to equalise value, but the rheological shear strains will have obviously different values.