The deformation and breakup of a power-law non-Newtonian slender drop in a Newtonian liquid in a simple shear and creeping flow has been theoretically studied. The problem is governed by three dimensionless parameters: The capillary number (Ca), the viscosity ratio (lambda), and the power-law index (n) of the non-Newtonian drop. The results show: (a) slender drops exist if n <= 1 only, these drops have pointed ends; (b) for the same strength of the flow, Newtonian drops are more elongated than shear thinning drops; and (c) for the same viscosity ratio, shear thinning drops are more difficult to break than Newtonian drops. (C) 2015 Elsevier B.V. All rights reserved.