After a detailed historical introduction, the author considers a rate-independent infinitesimal model, the loss of positiveness of symmetric part of acoustic tensor corresponding to local stability. Taking into account various bifurcation criteria for multisurface plasticity, the author determines plastic hardening moduli and their critical values together with critical orientation (for single surface plasticity, non-associative flow rules, and linear isotropic elasticity). The principal axes of second-order tensors of plastic potential and yield surfaces are coaxial. It is suggested that the critical orientations are identical for all principal directions, except for the case of double eigenvalues of plastic potential and yield surfaces. Some additional expressions are obtained for solids of Raniecki type. Examples concerning the loss of strong ellipticity and classical shear localization are compared for axially-symmetric compression and tension.