The entrance region flow in channels constitutes aproblem of fundamental interest in engineering applications such as nuclear reactors, polymer processing industries, haemodialyzersand capillary membrane oxygenators. In such installations, the behavior of the fluid in the entrance region may play a significant part in the total length of the channel and the pressure drop may bemarkedly greater than for the case where the flow is regarded asfully developed throughout the channel. Recently, there has been anincreasing interest in problems involving materials with variable viscosity such as Bingham materials, Casson fluids and Hershel-Bulkley fluids which are characterized by an yield value. The entrance region flow of a Casson fluid in an annular cylinder has been investigated numerically without making prior assumptions onthe form of velocity profile within the boundary layer region. This velocity distribution is determined as part of the procedure by crosssectional integration of the momentum differential equation for agiven distance z from the channel entrance. Using the macroscopicmass and momentum balance equation the entrance length has been obtained at each cross section of the entrance region of the annulifor specific values of Casson Number and various value of aspectratio. The effects of non-Newtonian characteristics and channel width on the velocity profile, pressure distribution and the entrancelength have been discussed.