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The constant Q property in viscoelastic media assumes that the quality factor Q does not change with frequency (i.e., the Q value is independent of the frequency). For seismic waves propagating in viscoelastic media, the wave equation is determined by the viscoelastic media model. Equivalence relations exist between various frequency domain mathematical models and physical rheological models for the constant Q property. Considering two elastic moduli and three attenuation variables, 24 kinds of wave equations based on different generalized rheological models are divided into six classes in this study, and the 12 kinds of specific representation for the wave equations in the time domain are derived. On the basis of the equivalence relations between the generalized rheological models, the difference and equivalence relation between different wave equations are proven and clarified. Results show that the high-order generalized rheological model can accurately characterize the attenuation characteristics of seismic waves and has advantages in characterizing the dispersion characteristics in viscoelastic media. Lastly, the seismic reflection characteristics caused by the difference of Q value are verified by the forward modeling of the constant Q wave equation in this study, thereby providing a theoretical basis for the analysis and inversion of the formation Q value from reflection seismic data.