In this study, the accuracy of the positional relationship of the contact between the inferior alveolar canal and mandibular third molar was evaluated using deep learning. In contact analysis, we investigated the diagnostic performance of the presence or absence of contact between the mandibular third molar and inferior alveolar canal. We also evaluated the diagnostic performance of bone continuity diagnosed based on computed tomography as a continuity analysis. A dataset of 1279 images of mandibular third molars from digital radiographs taken at the Department of Oral and Maxillofacial Surgery at a general hospital (2014–2021) was used for the validation. The deep learning models were ResNet50 and ResNet50v2, with stochastic gradient descent and sharpness-aware minimization (SAM) as optimizers. The performance metrics were accuracy, precision, recall, specificity, F1 score, and area under the receiver operating characteristic curve (AUC). The results indicated that ResNet50v2 using SAM performed excellently in the contact and continuity analyses. The accuracy and AUC were 0.860 and 0.890 for the contact analyses and 0.766 and 0.843 for the continuity analyses. In the contact analysis, SAM and the deep learning model performed effectively. However, in the continuity analysis, none of the deep learning models demonstrated significant classification performance.