Threshold of ribbing in a two-roll setup is investigated for non-Newtonian fluids. Two typical shear-thinning polymeric solutions are used, the first one exhibiting inelastic properties (Xanthan), the second one viscoelastic properties (polyacrylamide, PAAm). The effect of polymeric concentration and thus theological parameters on the effective critical capillary number Ca* at the onset of ribbing is described. For low polymer concentrations, only a small decrease of the onset is observed for both fluids. At larger concentrations, Ca* remains constant for inelastic fluids, while for the elastic fluids, a continuous decrease up to a factor 10, with respect to the Newtonian case, is observed. Above threshold, a strong effect on elastic properties is also observed on the amplitude of ribbing.