This paper presents an analysis of the laminar-turbulent transition for flow of yield-pseudoplastic fluids in pipes and concentric annuli. The yield-pseudoplastic rheology is represented by the three-parameter Robertson-Stiff model, A modified Reynolds number is developed based on an equivalent diameter including characteristic parameters of the flow situations under consideration. Using the literature data, Hanks' theory of laminar flow stability is reanalyzed in comparison with other correlations. On account of the generality of Hanks' stability criterion and its experimentally proven success to some extent, it is used herein to calculate critical values of the modified Reynolds number. Numerical results are presented in terms of the dimensionless rheological parameters and the annulus aspect ratio, Further, it is shown that constant critical value of Hanks' stability parameter (K-mc = 404) does not necessarily apply to non-Newtonian fluids. This fact is demonstrated for pipe flow of Bingham plastic fluids.