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In real systems there is always a certain amount of slip, which, however, is hard to detect experimentally because of the required space resolution. In this paper, we analyze the effect of slip boundary conditions on the dynamics of fluids in porous media by studying the flow of a Newtonian and non-Newtonian Maxwellian fluid in an axisymmetric cylindrical tube (pore), in which the flow is induced by traveling transversal waves on the tube wall. Like in peristaltic pumping, the traveling transversal waves induce a net flow of the liquid inside the pore. The viscosity as well as the compressibility of the liquid is taken into account. This problem has numerous applications in various branches of science, including stimulation of fluid flow in porous media under the effect of elastic waves and studies of blood flow dynamics in living creatures. The Navier-Stokes equations for an axisymmetric cylindrical pore are solved by means of a perturbation analysis, in which the ratio of the wave amplitude to the radius of the pore is small parameter. In the second order approximation, a net flow induced by the traveling wave is calculated for various values of the compressibility of the liquid, relaxation time and Knudsen number. The calculations disclose that the compressibility of the liquid, Knudsen number of slip flow and non-Newtonian effects in presence of peristaltic transport have a strong influence of the net flow rate. The effects of all parameters of the problem are numerically discussed and graphically explained. [ABSTRACT FROM AUTHOR]