A phase-field model is developed to study the formation and autocatalytic nucleation of {101¯2} twins in polycrystalline Mg. The twins are found to nucleate most favourably in grains with the most negative interaction energy. Within such grains, the energetically most favoured nucleation site is determined by stresses concentrated near the grain boundaries that are related to the elastic anisotropy of the material. Furthermore, in a structure consisting of three lamellar grains with an incoming twin in the central grain, the simulation results show that before autocatalytic nucleation, the incoming twin often has a lenticular shape. The stress field around the tip of the incoming twin plays the major role in the autocatalytic nucleation. After a twin has nucleated in the neighbouring grain, the incoming and the outgoing twins evolve simultaneously, and the shape of the incoming twin gradually changes from lenticular to parallel-sided plate. Under the condition that the crystallographic orientation of the central grain and the applied strain remains unchanged, the driving force for twin nucleation decreases with increasing misorientation (up to 90°) across the grain boundary. It is further derived that the interaction energy values between the pre-existing stress field of the polycrystalline structure and the eigenstrain of the to-be-nucleated twin is mathematically related to the resolved shear stress of twins. © 2018 Acta Materialia Inc.