One reason for the enduring interest in Newtonian fluid flow in Hele-Shaw cells is its close analogy to quasistatic solidification. The Saffman-Taylor ~ST! instability of the driven fluid-fluid interface plays the same role as the Mullins-Sekerka instability of the solidification front @1#. Features usually associated with solidification, such as the growth of stable dendritic fingers and sidebranching, have also been observed in fluids with an imposed anisotropy, say by scoring lines on the plates of the cell @2#. However, experiments using non-Newtonian or anisotropic fluids, such as liquid crystals, have shown that ‘‘solidification’’ structures can be induced by the bulk properties of the fluid itself @3‐5#. The precise mechanisms of generating such dendritic fingers with stable tips are unknown. One of our interests is in liquid crystal flows, which are characterized by complicated hydrodynamics @6#. We conjecture that stable tip propagation in these materials is a consequence of shear thinning associated with flow induced realignment of the liquid crystal director. In this paper we focus on this single property, and consider an expanding gas bubble in a radial HeleShaw cell containing a shear-thinning liquid. In recent work on polymeric fluids, Bonn and co-workers @7# proposed modeling the Hele-Shaw flow of a nonNewtonian fluid by positing the modified Darcy’s law