Although some organizations encourage employees to generate radical ideas by implementing stretch goals, the relationship between stretch goals and radical creativity is complicated. Unfortunately, existing research has not adequately addressed this issue. Therefore, we integrate signaling theory with creativity-related research and propose that the interaction between stretch goals and cognitive flexibility predicts employees' willingness to take risks, thereby influencing their engagement in radical creative activities and ultimately affecting their radical creativity. To test our hypotheses, we conduct two empirical studies. The results suggest that, for employees with high cognitive flexibility, stretch goals increase their willingness to assume risks, thus leading to improved engagement in radical creative activities and enhancing their radical creativity. Conversely, for employees with low cognitive flexibility, stretch goals decrease their willingness to take risks, which hampers their engagement in radical creative activities and their radical creativity. The theoretical contributions and practical implications of this study are also discussed.