This paper is concerned with the steady flow of a Maxwell fluid between two porous disks rotating with the same angular velocity about noncoincident axes normal to the disks. An exact solution to the problem depending on the Deborah number, the suction/injection velocity parameter, and the Reynolds number is obtained. It is shown that the core of fluid tends to rotate about the z-axis that characterizes the line in equal distance to the two axes of rotation when the Deborah and Reynolds numbers increase and a thinner boundary layer occurs in the region adjacent to the top disk when the axial velocity of fluid that is based on the suction/injection velocity parameter is upward. In addition, an approximate solution is presented for small Deborah numbers. The comparison between the exact and approximate solutions is given and found to be in excellent agreement.