The objective of this study is the development of an unsteady flow model of Rheologically complex fluid with fractal structure in various pipe geometries when the pressure is a harmonic function of time at a given frequency at the initial cross section of the pipe. The model was developed using scaling concepts in polymer physics. The obtained results show that the relaxation time and the fractal parameters can significantly influence the process of damping pressure along the pipe. It was demonstrated that depending on these parameters, the attenuation process may increase or decrease compared to the processes in a viscous damping fluid pressure. The results of simulations are compared to those for resin-asphalt-paraffin oils of two types produced in two oilfields.