A coupled problem of the evolution of the new phase domain in an elastic body with circular and elliptical hole due to stress-induced phase transformations is studied using a developed numerical procedure for simulating the interface propagation within the framework of the mechanics of configurational forces. A kinetic equation that specifies the dependence of the velocity of the interface on the configurational force, which is represented by the jump in the normal component of the Eshelby stress tensor, is used. The distributions of the configurational force along the interface are examined and presented as a tool for predicting interface evolution. First, various scenarios for the evolution of the new phase domain in a homogeneous body under external strain are demonstrated, both allowing and not allowing the existence of an equilibrium two-phase configuration. It is shown that the new phase domain can by itself act as a stress concentrator that induces further phase transformation. The variety of the interface behaviours in dependence on the distance between the interface and the concentrator, and the form of the concentrator are demonstrated based on examinations of the configurational force distribution along the interface. In the case of a circular hole, it is studied how the thickness of the new phase layer around the hole, affects the initial kinetics of the interface propagation. In the case of the phase transformation in the vicinity of an elliptical hole, the effects of the ratio of the semi-axes of the ellipse are examined. It is demonstrated how the elliptical hole can induce interface propagation even at external strain, which is insufficient for the existence of a new phase in the absence of the stress concentrator. It is studied how the shape and degree of localization of the new phase domain in the vicinity of the tip of the elliptical hole, as the prototype of the process zone in the vicinity of a crack tip, depend on the material parameters of the phases (Young’s moduli, Poisson‘s ratios, transformation strain). It is discussed how the new phase growth causes stress relaxation in a body based on examined stress distributions. Developed and verified algorithms and numerical modeling of the evolution of the new phase domain in the vicinity of the elliptical hole, including performed parametric analysis, can serve as the basis for subsequent studies of the joint propagation of the crack and the new phase domain.