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The classical flexure problem of non-linear incompressible elasticity isrevisited for elastic materials whose mechanical response is different intension and compression---the so-called bimodular materials. The flexureproblem is chosen to investigate this response since the two regions, one oftension and one of compression, can be identified easily using simpleintuition. Two distinct problems are considered: the first is where the stressis assumed continuous across the boundary of the two regions, which assumptionhas a sound physical basis. The second problem considered is more speculative:it is where discontinuities of stress are allowed. It is shown that suchdiscontinuities are necessarily small for many applications, but mightnonetheless provide an explanation for the damage incurred by repeated flexure.Some experimental evidence of the possibility of bimodularity in elastomers isalso presented.

Differences in tension and compression in the nonlinearly elastic bending of beams