Recently, in the fields of biosensing and nondestructive of materials, there are increasing interests on the investigations of the surface wave propagation in fluid loaded layered medium. Several different models for the elastic coefficients of viscous liquids are usually adopted in the investigations. The purpose of this paper is to study the variations of choosing different viscous liquid models on the dispersion and attenuation of waves in liquid loaded solids. In the paper, a derivation of the elastic coefficients of a viscous liquid based on the Stokes' assumption is given first. Then, for the hypothetical solid assumption of a viscous liquid, the associated wave equations and expressions of the stress components for different viscous liquid models utilized in the literatures are given. Finally, dispersion and attenuation of waves in a viscous liquid loaded A1 half space and a SiC plate immersed in a viscous liquid are calculated and utilized to discuss the differences among these four different models.