  The present study investigates novelties brought about into the classic
Biot's theory of propagation of elastic waves in a fluid-saturated porous solid
by inclusion of non-Newtonian effects that are important, for example, for
hydrocarbons. Based on our previous results (Tsiklauri and Beresnev: 2001,
Phys. Rev. E, 63, 046304), we have investigated the propagation of rotational
and dilatational elastic waves, through calculating their phase velocities and
attenuation coefficients as a function of frequency. We found that the
replacement of an ordinary Newtonian fluid by a Maxwell fluid in the
fluid-saturated porous solid results in: (a) an overall increase of the phase
velocities of both the rotational and dilatational waves. With the increase of
frequency these quantities tend to a fixed, higher, as compared to the
Newtonian limiting case, level which is not changing with the decrease of the
Deborah number $\alpha$. (b) the overall decrease of the attenuation
coefficients of both the rotational and dilatational waves. With the increase
of frequency these quantities tend to a progressively lower, as compared to the
Newtonian limiting case, levels as $\alpha$ decreases. (c) Appearance of
oscillations in all physical quantities in the deeply non-Newtonian regime.
