To understand the abnormal flow conditions caused by the presence of stenoses in arteries, an analytical solution is obtained for the steady laminar flow of an incompressible Newtonian fluid in an axisymmetric conduit with irregular surface where the spread of the surface roughness is large compared with the mean radius of the conduit. Numerical results are presented for the streamlines, the distributions of velocity, vorticity, and pressure, the energy dissipation, and the separation and reattachment points for conduits with sinusoidal wall variations. The analysis is also applicable to a locally constricted conduit, provided the separation zone does not extend into the straight wall portion of the conduit.