Surface wave measurements have been used to compute the dynamic soil properties for near surface site characterization and the dynamic design of foundations. Much of this work has been done with the Rayleigh waves which are dependent on both the shear and the compressive wave properties of the soil. Love waves,on the other hand, are sensitive only to the shear wave response of the soil. This shear only sensitivity greatly simplifies determining the damping and the stiffness of a near surface soil profile. Further, the mechanism of damping can be related to purely inertial interactions of the soil frame and the pore fluids, free from compressive factors. Traditionally, soils have been represented by elastic models. While elastic models are adequate in representing dry or impermeable soils, they fail to account for the observed down-hole body wave dispersion in permeable, water saturated soils. To overcome this limitation, a viscoelastic model can be used. In this work, a viscoelastic representation of the Love wave propagation is derived for the forward problem. The solution to this forward problem yields the dispersion and the attenuation curves. Also computed are the complex motion-stress vectors fora vertically heterogeneous, viscoelastic medium, with the shear viscosity as a specific material property. The viscoelastic constitutive model will lead to an improved representation of Love wave propagation in permeable,water saturated soils where the concept of the effective viscosity becomes inappropriate.