  Mechanical stress within biological tissue can indicate an anomaly, or can be
vital of its function, such as stresses in arteries. Measuring these stresses
in tissue is challenging due to the complex, and often unknown, nature of the
material properties. Recently, a method called the angled shear wave identity
was proposed to predict the stress by measuring the speed of two small
amplitude shear waves. The method does not require prior knowledge of the
material's constitutive law, making it ideal for complex biological tissues. We
extend this method, and the underlying identity, to include viscous
dissipation, which can be significant for biological tissues. To generalise the
identity, we consider soft viscoelastic solids described by a generalised
Newtonian viscous stress, and account for transverse isotropy, a feature that
is common in muscle tissue, for instance. We then derive the dispersion
relationship for small-amplitude shear waves superimposed on a large static
deformation. Similarly to the elastic case, the identity is recovered when the
stress in the material is coaxial with the transverse anisotropy. A key result
in this paper is that to predict the stress in a viscous material one would
need to measure the wave attenuation as well as the wave speed. The case of
viscoelastic materials with memory is also discussed.
