This paper analyzes propagating wave solutions of the linearized barotropic vorticity equation near a critical level in a north-south flow V (x). The long Rossby wave found to the west of a wave source passes through the critical level unaffected. The short Rossby wave found to the east of a source is attenuated across the critical level by a factor exp (-&pgr;β/lV'), where l is the north-south wave number and V' the shear at the critical level. Wave velocity components (u, &ngr;) do not become infinite near the critical level. Numerical solutions show how Rossby wave propagation on a large-scale domain is affected by critical level absorption. Implications for ocean basin models where phenomena depend on Rossby wave reflection at a western boundary are discussed.