Darwin’s finches are a model system for studying adaptive diversification. However, despite the large body of work devoted to this system, rather little is known about the functional consequences of variation in the size and shape of bills. We test, using two methods, if natural or sexual selection, or both, has resulted in functional divergence in bill and head morphology. Firstly, we compare data on head-shape and bite-forces across nine species of Darwin’s finches. Secondly, we use micro-CT scans and finite-element models to test the prediction that the shape of the bill in representatives of the different feeding types is adaptively related to use of the bill. Sexual dimorphism in head-shape and bite-force was detected, with females having longer bills than males for a given body size. Moreover, our results show strong differences in bill- and head-morphology between feeding types, with base-crushers having higher bite-forces and also relatively high bite-forces at the tip compared to probers and tip-biters. Finally, our finite-element models suggest that the shape of the bill in the tip-biters and base-crushers confers mechanical advantages by minimising stress in tip-loading and base-loading conditions, respectively, thus reducing probabilities of fracture. Our data support the contention that bill-shape is adaptive and evolves under selection for mechanical optimisation through natural selection on feeding mode.