Rubber components and soft biological tissues are often subjected to large bending deformations while “in service”. The circumferential line elements on the inner face of a bent block can contract up to a certain critical stretch ratio λ_cr (say) before bifurcation occurs and axial creases appear. For several models used to describe rubber, it is found that λ_cr=0.56, allowing for a 44% contraction. For models used to describe arteries it is found, somewhat surprisingly, that the strain-stiffening effect promotes instability. For example, the models used for the artery of a seventy-year old human predict that λ_cr=0.73, allowing only for a 27% contraction. Tensile experiments conducted on pig skin indicate that bending instabilities should occur even earlier there.