This paper presents an original approach based on evolutionary algorithms for building structures that are stable under gravity for the physics-based puzzle game Angry Birds, with the ultimate objective of creating Angry Birds levels with the minimum number of constraints. We have created a custom open source evolutionary computation library that implement an evolutionary algorithm whose main challenges have been to design a fitness function that, first, avoids when possible the time-consuming actual execution of the game, and, then, takes into account the different ways in which a structure is not sound and eliminates them. In order to test the method six experiments have been carried out, obtaining a variety of stable structures, which is the first path for the generation of levels that are aesthetically pleasing as well as playable.