Stability of plastic deformation at the level of a homogeneous material element imbedded in a deforming continuum is discussed. Distinction is made between instability of equilibrium and instability of uniform straining of the element. Under the general assumption that constitutive rate equations admit a potential, pointwise energy criteria of instability are formulated and related to propagation of acceleration waves and to incipient localization of deformation. For incrementally nonlinear materials they are shown to differ in general from the familiar condition of ellipticity loss. Existence of a continuous range of shear band bifurcations is demonstrated. In a numerical example, a finite strain version of the Christoffersen-Hutchinson model of material behaviour at a yield-surface vertex is used.