Large pre-trained language models achieve state-of-the-art results when fine-tuned on downstream NLP tasks. However, they almost exclusively focus on text-only representation, while neglecting cell-level layout information that is important for form image understanding. In this paper, we propose a new pre-training approach, StructuralLM, to jointly leverage cell and layout information from scanned documents. Specifically, we pre-train StructuralLM with two new designs to make the most of the interactions of cell and layout information: 1) each cell as a semantic unit; 2) classification of cell positions. The pre-trained StructuralLM achieves new state-of-the-art results in different types of downstream tasks, including form understanding (from 78.95 to 85.14), document visual question answering (from 72.59 to 83.94) and document image classification (from 94.43 to 96.08).