This paper describes numerical solutions for the laminar flow of non-Newtonian fluids in vertical annuli using the Herschel-Bulkley model to describe the rheological behaviour of such materials. Numerical solutions have been obtained when there is both axial and tangential flows in either a concentric or eccentric annulus. The tangential flow arises from the rotation of the inner cylinder of the annulus and the axial flow from a constant axial pressure gradient. The flow is analysed by solving the momentum and continuity equation numerically using the finite element method. The dimensionless velocity, deformation and stress profiles with other quantities such as the apparent viscosity and pressure distribution have been calculated for various eccentricities, radius ratios, fluid properties and flow parameters; the results give insights into the flow behaviour in the annuli. It is shown that the inclusion of rotational effects, for a fixed pressure gradient, is likely to increase the axial volumetric flowrate over non-rotating situations in concentric geometries. New results reveal that, in eccentric annuli, the situation is reversed and the flowrate gradually decreases as the rotation rate is increased.