  We extend the theory of complete Bernstein functions to matrix-valued
functions and apply it to analyze Green's function of an anisotropic
multi-dimension\-al linear viscoelastic problem. Green's function is given by
the superposition of plane waves. Each plane wave is expressed in terms of
matrix-valued attenuation and dispersion functions given in terms of a
matrix-valued positive semi-definite Radon measure. More explicit formulae are
obtained for 3D isotropic viscoelastic Green's functions. As an example of an
anisotropic medium the transversely isotropic medium with a constant symmetry
axis is considered.
