a b s t r a c tWe have shown in a previous paper that twin boundary area fraction in lamellar g-TiAl based alloys depends on collective or correlated nucleation induced by long-range elastic interactions among nucleating precipitates or between pre-existing and nucleating precipitates. In this study we investigate the effects of applied stresses on g nucleation and evolution by elastic interaction energy calculations and phase field simulations. It is found that the elastic interaction energy reaches minimum when two variants are twin related because of their self-accommodation of the coherency strain. When external stresses are present, such autocatalysis during nucleation could be either enhanced or suppressed.Compression perpendicular or tension parallel to the basal plane of the a phase is found to enhance the internal elastic interactions between nucleating precipitates, promote twin variant selection and reduce the overall nucleation rate, while isostatic pressing, compression parallel, tension perpendicular to the basal plane does the opposite. Shear along the interface always reduce the twin boundary area fraction, regardless of the shear direction. These findings could shed light on optimizing processing routes to increase twin boundary area fraction in lamellar microstructures of g-TiAl based alloys.