We analyzed the effect of viscoelasticity on the dynamics of fluids in poro
us media by studying the flow of a Maxwell fluid in a circular tube, in whi
ch the flow is induced by a wave traveling on the tube wall. The present pa
per investigates phenomena brought about into the classic peristaltic mecha
nism by inclusion of non-Newtonian effects that are important, e.g., for hy
drocarbons. This problem has numerous applications in various branches of s
cience, including the stimulation of fluid flow in a porous media under the
effect of elastic waves and studies of blood flow dynamics in living creat
ures. We have found that in the extreme non-Newtonian regime, there is a po
ssibility of a fluid flow in the direction opposite to the propagation of t
he wave traveling on the tube wall.