Abstract The thermomechanical theory of phase transitions (PT) developed by Levitas (Part I of the paper) is extended to the case with displacement discontinuities across an interface (noncoherence and fracture). Two boundary-value problems are solved analytically: the appearance of a spherical nucleus in an infinite elastoplastic sphere under applied pressure (without or with interfacial fracture) with application to temperature-induced PT in steel and pressure-induced PT graphite-diamond; noncoherent PT in a rigidplastic half-space. The effect of strain hardening on the PT condition is discussed. The experimental phenomena described in the paper are enumerated. Results of the numerical modelling of the technological process of diamond synthesis are discussed in connection with the explanation of experimental results and revelation of the pressure self-regulation effect. Some methods for the control of PT by means of the purposeful control of stress-strain fields are suggested, using analysis of various useful examples of stress field variation during PT in the problems solved in Parts I and II.