Abstract. This paper investigates the possibility of kinematic interfacial instabilities occurring during the industrial process of primary cementing of oil and gas wells. This process involves to flows in narrow eccentric annuli that are modelled via a Hele-Shaw approach. The fluids present in primary cementing are strongly non-Newtonian, usually exhibiting shear-thinning behaviour and often with a yield stress. The study is a sequel to [1] in which the base analysis has been developed for the case of 2 Newtonian fluids. The occurrence of static mud channels in primary cementing has been known of since the 1960's, [2], and is a major cause of process failure. We quantify this phenomenon, providing a simple semi-analytic expression for the maximal volume of residual fluid left behind in the annulus, f static , and illustrate the dependency of fstatic on its five dimensionless parameters. We show that 3 of the 4 different types of static channel flows are linearly stable.Via dimensional analysis, we show that the base flows depend on a minimal set of 8 dimensionless parameters and the stability problem depends on an additional 3 dimensionless parameters. This large dimensional parameter space precludes use of the full numerical solution to the stability problem as a predictive tool or for studying the various stability regimes. Instead we have developed a semi-analytical approach based on solution of the long wavelength limit. This stability results can be evaluated via simple quadrature from the base flow and is suitable for use in process optimisation.