Orthodontics is the branch of dentistry that focuses on the study and treatment of malocclusions. Orthodontic treatments commonly involve the insertion of an archwire made from stainless steel or an alloy onto orthodontic brackets, thereby inducing movement of teeth into desired positions. However, archwire activation may also induce undesirable tooth rotation because of the applied moment. Appropriate magnitude of gable bend in archwires will prevent unwanted rotation. However, the relationship between rotation and gable bend cannot be easily determined. This study presents a numerical approach to predict tooth rotation with respect to gable bend upon archwire activation. The kriging interpolation method is introduced to predict tooth rotation, thus leading to suggestions in optimum bending angles by minimizing undesirable tooth rotations. Optimization is performed based on reliable kriging models.