Abstract: To describe the behavior of the viscous oil-bearing reservoir, a viscous-porous model is proposed in view of the liquid viscoelastic constitutive relation, and also, its elastic wave equations are presented. Through dimension analysis of dispersive relationships of dilatational waves and rotational waves, the characteristic frequency at which the slow shear wave exists is deduced, which provides theoretical evidence to record the slow shear wave in future. Numerical analyzes are performed to study the changing of the phase velocity and the attenuation of the four elastic waves with porosity and frequency. The results show that the slow S-wave propagates mainly in the porous fluid and the phase velocity of the slow S-wave is fast in the porous media with low porosity and high frequency.