SUMMARYThe ow inside a spatially modulated channel is examined for viscoelastic uids of the Oldroyd-B type. The lower wall is at and the upper wall is sinusoidally modulated. The modulation amplitude is assumed to be small. Thus, a regular perturbation expansion of the ow 每eld coupled to a variable-step 每nite-di erence scheme is used to solve the problem. Convergence and accuracy assessment against earlier experimental results indicate that there is a signi每cant range of validity of the perturbation approach. The in uences of wall geometry, inertia and viscoelasticity on the ow kinematics and stresses are investigated systematically. In particular, the interplay between the ow and uid parameters e ects on the conditions for the onset of back ow, number of vortices, their size and location is revealed. The distance between the ow separation and reattachment locations identi每es the vortex size. Nonmonotonic dependence of the vortex size on elasticity is reported. The critical conditions for the onset of negative elasticity e ects on vortex size are identi每ed. The critical Reynolds number for the onset of back ow initially decreases then levels o or even increases as elasticity increases. For highly elastic uid and large enough Reynolds number, more than one vortex appear near the lower wall.