The flow of non-Newtonian fluids in annular geometries is an important problem, especially for the extrusion of polymeric melts and suspensions and for oil and gas exploration. Here, an analytical solution of the equation of motion for the axial flow of an incompressible viscoplastic fluid (represented by the Hershel-Bulkley equation) in a long concentric annulus under isothermal, fully developed, and creeping conditions and subject to true or apparent wall slip is provided. The simplifications of the analytical model for Hershel-Bulkley fluid subject to wall slip also provide the analytical solutions for the axial annular flows of Bingham plastic, power-law, and Newtonian fluids with and without wall slip at one or both surfaces of the annulus.