Abstract In this paper we develop conditions that govern the evolution of a fully faceted interface separating elastic phases. To focus attention on the effects of elastic stress, we restrict attention to interface-controlled kinetics, neglecting bulk transport; and to avoid geometric complications, we limit our discussion to two space-dimensions. We consider a theory in which the orientations present on the evolving particle are not necessarily those given by the Wulff shape: we allow for metastable crystallographic orientations as well as stable orientations. We find that elastic stress affects the velocity of a facet through the average value of the normal component of the jump in configurational stress (Eshelby stress) over the facet. Within our theory singularities in stress induced by the presence of corners do not influence the velocity of the facet. We discuss the nucleation of facets from corners; the resulting nucleation condition is shown to be independent of elastic stress. We also develop equations governing the equilibrium shape of a faceted particle in the presence of elastic stress.