Nonlinear effects have been considered in computations of orthogonal rheometer flow and in flow caused by the oscillation of a sphere in an unbounded fluid. Predictions of fluid response, based on a Bird‐Carreau constitutive model, are qualitatively different from those which follow from linear theory. Of particular interest are the corrections to force components in the orthogonal rheometer analysis and the generation of a steady secondary flow in the oscillating sphere problem. Magnitudes of these nonlinear effects are presented for a variety of fluid and flow parameters.