Unsteady flow of a viscous, incompressible fluid in a semi-infinte circular tube with a porous, elastic wall whose length varies with time, but whose cross-section does not vary, is studied considering the effects of suction or injection on the wall. Laminar, similar solutions with respect to space and time are obtained. Velocities, pressure, drag, power and work of fluid are analyzed. There are the critical conditions of suction and injection on the wall in accordance with the conditions of motion of the wall either contracting or expanding in an axial direction. The conditions of suction and injection are divided into two parts, giving a classification of the situations of the induced flow fields.