Plate fixation is a common treatment option for radial head fractures (RHFs). Due to the benefits of less invasiveness and fewer complications of internal fixation, the application of small-diameter headless compression screws (HCSs) to treat RHFs has become a new trend. This study aimed to compare the mechanical stability of four distinct internal fixation protocols for transversely unstable RHFs via finite element analysis. Using computed tomography data from 10 patients, we developed 40 patient-specific FE models of transversely unstable RHFs fixed by parallel, crossed, and tripod HCSs and mini-T plate (MTP). Under simulated physiological loading of the elbow joint, the construct stiffness, displacement, and von Mises stresses were evaluated and verified by a biomechanical experiment. Under shear loading, the MTP group exhibited lower construct stiffness, larger displacement, and higher Von Mises stress than the HCSs group. The stiffness of tripod HCSs was greater than parallel and crossed screw fixation techniques. There was a strong relationship between apparent bone density and construct stiffness (R = 0.98 to 0.99). In the treatment of transversely unstable RHFs, HCSs have superior biomechanical stability than MTP. The tripod technique was also more stable than parallel and crossed fixation.