The baculum (os penis) is a mineralized bone within the glans of the mammalian penis and is one of the most morphologically diverse structures in the mammal skeleton. Recent experimental work provides compelling evidence for sexual selection shaping the baculum, yet the functional mechanism by which this occurs remains unknown. Previous studies have tested biomechanical hypotheses for the role of the baculum based on simple metrics such as length and diameter, ignoring the wealth of additional shape complexity present. For the first time, to our knowledge, we apply a computational simulation approach (finite-element analysis; FEA) to quantify the three-dimensional biomechanical performance of carnivoran bacula (n= 74) based upon high-resolution micro-computed tomography scans. We find a marginally significant positive correlation between sexual size dimorphism and baculum stress under compressive loading, counter to the ‘vaginal friction’ hypothesis of bacula becoming more robust to overcome resistance during initial intromission. However, a highly significant negative relationship exists between intromission duration and baculum stress under dorsoventral bending. Furthermore, additional FEA simulations confirm that the presence of a ventral groove would reduce deformation of the urethra. We take this as evidence in support of the ‘prolonged intromission’ hypothesis, suggesting the carnivoran baculum has evolved in response to pressures on the duration of copulation and protection of the urethra.