A block of rubber eventually buckles under severe flexure, and several axial wrinkles appear on the inner curved face of the bent block. Experimental measurements reveal that the buckling occurs earlier - at lower compressive strains - than expected from theoretical predictions. This paper shows that if rubber is modeled as being bimodular, and specifically, as being stiffer in compression than in tension, then flexure bifurcation happens indeed at lower levels of compressive strain than predicted by previous investigations (these included taking into account finite size effects, compressibility effects, and strain-stiffening effects). Here the effect of bimodularity is investigated within the theory of incremental buckling, and bifurcation equations, numerical methods, dispersion curves, and field variations are presented and discussed. It is also seen that Finite Element Analysis software seems to be unable to encompass in a realistic manner the phenomenon of bending instability for rubber blocks. (C) 2009 Elsevier Ltd. All rights reserved.