In tetrapods, fusion between elements of the appendicular skeleton is thought to facilitate rapid movements during running, flying, and jumping. Although such fusion is widespread, frogs stand out because adults of all living species exhibit fusion of the zeugopod elements (radius and ulna, tibia and fibula), regardless of jumping ability or locomotor mode. To better understand what drives the maintenance of limb bone fusion in frogs, we use finite element modeling methods to assess the functional consequences of fusion in the anuran radioulna, the forearm bone of frogs that is important to both locomotion and mating behavior (amplexus). Using CT scans of museum specimens, measurement tools, and mesh-editing software, we evaluated how different degrees of fusion between the radius and ulna affect the von Mises stress and bending resistance of the radioulna in three loading scenarios: landing, amplexus, and long-axis loading conditions. We find that the semi-fused state observed in the radioulna exhibits less von Mises stress and more resistance to bending than unfused or completely fused models in all three scenarios. Our results suggest that radioulna morphology is optimized to minimize von Mises stress across different loading regimes while also minimizing volume. We contextualize our findings in an evaluation of the diversity of anuran radioulnae, which reveals unique, permanent pronation of the radioulna in frogs and substantial variation in wall thickness. This work provides new insight into the functional consequences of limb bone fusion in anuran evolution.