This paper investigates the application of deep learning-based natural language processing techniques in modern Mongolian legal documents. In particular, we explore several methods that apply Bidirectional Encoder Representations from Transformers (BERT) models for classifying modern Mongolian legal documents. Based on our findings, we propose BERT-based models called LEGAL-BERT-Mongolian. We demonstrated two variants of LEGAL-BERT-Mongolian, i.e., uncased-LEGAL-BERT-Mongolian and cased-LEGAL-BERT-Mongolian, for classifying modern Mongolian legal documents. The uncased-LEGAL-BERT-Mongolian model achieved the best results, with a precision of 0.91, recall of 0.87, and F1 score of 0.89, whereas the cased-LEGAL-BERT-Mongolian model achieved a precision of 0.87, recall of 0.83, and F1 score of 0.85.