Studies of wave attenuation and dispersion in heterogeneous porous materials caused by fluidsolid interactions are often based on Biot’s equations of poroelasticity (Biot 1956a,b, 1962). This theory has been further developed by Spanos & de la Cruz (1985), Sahay et al. (2001) and Spanos (2002). These authors used the volume-averaging technique to upscale the pore-scale equations. More recently, Sahay (2008) analyzed the consequences of incorporating the fluid strain rate tensor into Biot’s constitutive relation as is suggested within the volume-averaging framework. This guarantees that by tending porosity to unity, the constitutive relation render a Newtonian fluid. We refer to this framework as the viscosity-extended Biot framework. A particularity of this extended framework is the prediction of an additional shear mode with non-vanishing velocity, which essentially describes the out-of-phase shear motions of the two phases. In the classical Biot theory, it is a non-propagating process as a result of the neglect of viscous stresses in the fluid phase. In analogy to the second or slow compressional wave of the Biot theory we refer to this second shear wave as slow shear wave (see also Mavko et al. 2009).