Shear band formation is an example of a material instability, corresponding to an abrupt loss of homogeneity of deformation occurring in a solid sample subject to a loading path compatible with continued uniform deformation. In this sense, it may be interpreted as a deformation mechanism ‘alternative’ to a trivial one and therefore a bifurcation or loss of uniqueness of a ‘perfect’ equilibrium path. The distinctive character of this bifurcation is that it may occur even in an infinite body (or under the extreme constraint of smooth contact with a rigid constraint).