The superposition of a circular Couette flow and a pressure- driven axial flow in an annulus occurs in many practical applications, such as catalytic chemical reactors, filtration devices, liquid-liquid extractors, journal bearings, and the return flow of drilling mud between the rotating drill string and the stationary wall in oil and gas well drilling. The curved streamlines of the circular Couette flow can cause a centrifugal instability leading to toroidal vortices, well known as Taylor vortices. The presence of these vortices changes the hydrodynamic and heat transfer characteristics of the process. Therefore, it is very important to be able to predict the onset of instability. Most of the available theoretical and experimental analyses are for Newtonian and viscoelastic (polymeric solutions) liquids. In this work, the effect of the viscoplastic properties of high concentration suspensions on the onset of the Taylor vortices are determined theoretically by solving the conservation equations and searching the critical conditions. The differential equations were solved by the Galerkin / finite element method and the resulting set of non-linear algebraic equations, by Newtons method.