Social anxiety is a prevalent psychological issue among college students, severely impairing their mental health and executive functioning. This study employed three executive function-related experimental paradigms—Go/No-go (inhibitory control), task-switching (cognitive flexibility), and N-back (working memory)—to collect behavioral and electroencephalogram (EEG) data from college students. Artificial intelligence methods, including machine learning and deep learning techniques, were applied to explore objective identification approaches for individuals with social anxiety. Results demonstrated that when using only behavioral data for classification, deep learning models outperformed traditional and ensemble machine learning models (e.g., Support Vector Machine, Random Forest). Similarly, deep learning models exhibited significant advantages in EEG data classification. Notably, the multimodal deep learning model (BEPTCNN) integrating behavioral and EEG data achieved optimal performance across all evaluation metrics. This indicates that multimodal data fusion provides richer information, enhancing diagnostic accuracy for social anxiety. The findings strongly support the development of AI-based diagnostic tools for social anxiety and lay a foundation for further elucidating its physiological mechanisms and improving intervention strategies. Future research should explore the generalizability and interpretability of deep learning models, as well as their potential application in real-time diagnostic systems.