Darwin's finches have radiated from a common ancestor into 14 descendent species, each specializing on distinct food resources and evolving divergent beak forms. Beak morphology in the ground finches (Geospiza) has been shown to evolve via natural selection in response to variation in food type, food availability and interspecific competition for food. From a mechanical perspective, however, beak size and shape are only indirectly related to birds' abilities to crack seeds, and beak form is hypothesized to evolve mainly under selection for fracture avoidance. Here, we test the fracture-avoidance hypothesis using finite-element modelling. We find that across species, mechanical loading is similar and approaches reported values of bone strength, thus suggesting pervasive selection on fracture avoidance. Additionally, deep and wide beaks are better suited for dissipating stress than are more elongate beaks when scaled to common sizes and loadings. Our results illustrate that deep and wide beaks in ground finches enable reduction of areas with high stress and peak stress magnitudes, allowing birds to crack hard seeds while limiting the risk of beak failure. These results may explain strong selection on beak depth and width in natural populations of Darwin's finches.