The tendon-to-bone attachment site integrates two distinct tissues via a gradual transition in composition, mechanical properties, and structure. Outcomes of surgical repair are poor, in part because surgical repair does not recreate the natural attachment, and in part because the mechanical features that are most critical to mechanical and physiological function have not been identified. We employed allometric analysis to resolve a paradox about how the architecture of the rotator cuff contributes to load transfer: whereas published data suggest that the mean muscle stresses expected at the tendon-to-bone attachment are conserved across species, data also show that the relative dimensions of key anatomical features vary dramatically, suggesting that the amplification of stresses at the interface between tendon and bone should also vary widely. However, a mechanical model that enabled a sensitivity analysis revealed that the degree of stress concentration was in fact highly conserved across species: the factors that most affected stress amplification were most highly conserved across species, while those that had a lower effect showed broad variation across a range of relative insensitivity. Results highlight how micromechanical factors can influence structure-function relationships and cross-species scaling over several orders of magnitude in animal size, and provide guidance on physiological features to emphasize in surgical and tissue engineered repair of the rotator cuff.