The problem of steady incompressible laminar flow of elasticoviscous liquids through a cylindrical annulus in the presence of suction and injection is considered. The rate of suction at one wall is taken to be equal to the rate of injection at the other wall of the annulus. Perturbation method is used for the axial velocity regardingS = R Rcas the perturbation parameter. For rapid convergence of the series solution,Sis taken to be equal to 0.1. The effects of cross‐flow Reynolds numberRand elastic numberRcon the components of velocity and the pressure fields are shown graphically.