This paper investigates the suitability of using Generative Adversarial Networks (GANs) to generate stable structures for the physics-based puzzle game Angry Birds. While previous applications of GANs for level generation have been mostly limited to tile-based representations, this paper explores their suitability for creating stable structures made from multiple smaller blocks. This includes a detailed encoding/decoding process for converting between Angry Birds level descriptions and a suitable grid-based representation, as well as utilizing state-of-the-art GAN architectures and training methods to produce new structure designs. Our results show that GANs can be successfully applied to generate a varied range of complex and stable Angry Birds structures.