Although there are five effective shear moduli for any layered VTI medium, the main result of the paper is that there is just one effective shear modulus for the layered system that contains all the dependence of pore fluids on the elastic or poroelastic constants -- all that can be observed in vertically polarized shear waves in VTI media. The relevant modulus Geff is related to uniaxial shear strain and the relevant axis of symmetry is the vertical one, normal to the bedding planes. The pore-fluid effects on this effective shear modulus can be substantial when the medium behaves in an undrained fashion, as might be expected at higher frequencies such as sonic and ultrasonic for well-logging or laboratory experiments, or at seismic frequencies for lower permeability regions of reservoirs. These predictions are clearly illustrated by the example in Figure 2.