This research investigates the hydro dynamical features of steady rectilinear torsional flow of pseudoplastic fluid between two infinite coaxial cylinders. Rotation of both cylinders about common axis yields the motion in the fluid. Three cases has been considered i.e. (i) when the inner cylinder rotates and the outer cylinder is at rest, (ii) when the outer cylinder is rotated, and inner is at rest and (iii) when the inner is rotated, and outer is removed. Governing equation describing the flow of pseudoplastic fluid has been derived and analytical solution are obtained by employing Langlois Recursive Approach (Langlois, 1963). Analytical solution for velocity profile of rotating cylinders and its special cases are calculated up to third order. The corresponding solution for viscous fluid is obtained as a limiting case. The impact of various evolving parameter on the flow, i.e. angular velocity (ω), radius ratio (R), gap width (r) and non-Newtonian parameter (β) are examined and illustrated graphically. The analytical approximate solutions acquired are in accordance with the existing literature if the non-Newtonian behaviors vanishes.
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