  In this paper we discuss the uniaxial propagation of transient waves within a
semi-infinite viscoelastic Bessel medium. First, we provide the analytic
expression for the response function of the material as we approach the
wave-front. To do so, we take profit of a revisited version of the so called
Buchen-Mainardi algorithm. Secondly, we provide an analytic expression for the
long time behavior of the response function of the material. This result is
obtained by means of the Tauberian theorems for the Laplace transform. Finally,
we relate the obtained results to a peculiar model for fluid-filled elastic
tubes.
