Positional cranial deformities are relatively common conditions, characterized by asymmetry and changes in skull shape. Although three-dimensional (3D) scanning is the gold standard for diagnosing such deformities, it requires expensive laser scanners and skilled maneuvering. We therefore developed an inexpensive, fast, and convenient screening method to classify cranial deformities in infants, based on single two-dimensional vertex cranial images. In total, 174 measurements from 80 subjects were recorded. Our screening software performs image processing and machine learning-based estimation related to the deformity indices of the cranial ratio (CR) and cranial vault asymmetry index (CVAI) to determine the severity levels of brachycephaly and plagiocephaly. For performance evaluations, the estimated CR and CVAI values were compared to the reference data obtained using a 3D cranial scanner. The CR and CVAI correlation coefficients obtained via support vector regression were 0.85 and 0.89, respectively. When the trained model was evaluated using the unseen test data for the three CR and three CVAI classes, an 86.7% classification accuracy of the proposed method was obtained for both brachycephaly and plagiocephaly. The results showed that our method for screening cranial deformities in infants could aid clinical evaluations and parental monitoring of the progression of deformities at home.