  Finite propagation speed properties in mathematical elastic and viscoelastic
models are fundamental in many applications where the data exhibits propagating
fronts. We note particularly that this property is observed in biomechanical
imaging of tissue, in particular in the supersonic imaging experiment, and also
in geophysics and ocean acoustics. With these applications in mind, noting that
there are many other applications as well, we present finite propagation speed
results for very general integro-differential, anisotropic, viscoelastic linear
models, which are not necessarily of convolution type. We start with work
density, define work density decomposition and we achieve our results utilizing
energy arguments. One of the advantages of our presented method, instead of
using plane wave arguments, is that there is no need to make the homogeneous
medium assumption to obtain the finite propagation speed results.
