Local and global uniqueness and stability criteria were introduced in Chapters 10 and 11, with reference to non-associative elastoplasticity (Chapter 8). The incremental non-linearity of the rate-constitutive equations of plasticity and the lack of symmetry connected to the flow-rule non-associativity strongly complicate the bifurcation and instability analyses with respect to the case of incremental elasticity. Therefore, despite interest in the applications to bifurcation problems for geological and quasibrittle materials, there have been only a few attempts to apply the comparison solids methodology to bifurcation problems (Bruhns and Raniecki, 1982; Kleiber, 1984; 1986; Tomita et al., 1988; Bigoni, 2000), so our interest in this chapter is to provide examples of the methodologies explained in Chapters 10 and 11. We will use the simplest constitutive setting, which is that of small strain Drucker-Prager elastoplasticity with deviatoric associativity, a context in which we will limit examples to local stability criteria, whereas the use of Raniecki comparison solids will be presented for a simple elastoplastic non-associative model at large strain.