Visually-rich Document Understanding (VrDU) has attracted much research attention over the past years.Pre-trained models on a large number of document images with transformer-based backbones have led to significant performance gains in this field.The major challenge is how to fusion the different modalities (text, layout, and image) of the documents in a unified model with different pre-training tasks. This paper focuses on improving text-layout interactions and proposes a novel multi-modal pre-training model, LayoutMask.LayoutMask uses local 1D position, instead of global 1D position, as layout input and has two pre-training objectives: (1) Masked Language Modeling: predicting masked tokens with two novel masking strategies; (2) Masked Position Modeling: predicting masked 2D positions to improve layout representation learning.LayoutMask can enhance the interactions between text and layout modalities in a unified model and produce adaptive and robust multi-modal representations for downstream tasks.Experimental results show that our proposed method can achieve state-of-the-art results on a wide variety of VrDU problems, including form understanding, receipt understanding, and document image classification.