The steady‐state laminar flow of an incompressible elasticoviscous liquid in an annulus with coaxial porous walls, rotating about a common axis is considered. The rate of fluid injection at one wall is taken to be equal to the rate of fluid suction at the other. The flow phenomenon has been characterized by the nondimensional parametersRc(elastic number),R(cross‐flow Reynolds number),m(ratio of the angular velocities of the cylinders), and &sgr; (radii ratio). A small perturbation method has been used to obtain an approximate solution for the velocity field. The perturbation method is in powers ofRand, thus, valid for sufficiently small |R|, but generalRc. A perturbation method in powers ofRchas also been used to obtain an approximate solution of the velocity field. This solution should be valid for sufficiently small|Rc|but generalR. The effects of the above parameters on the velocity distribution, shear stress at the walls, and the radial pressure variation have been studied.