The segment anything model (SAM) was released as a foundation model for image segmentation. The promptable segmentation model was trained by over 1 billion masks on 11M licensed and privacy-respecting images. The model supports zero-shot image segmentation with various segmentation prompts (e.g., points, boxes, masks). It makes the SAM attractive for medical image analysis, especially for digital pathology where the training data are rare. In this study, we evaluate the zero-shot segmentation performance of SAM model on representative segmentation tasks on whole slide imaging (WSI), including (1) tumor segmentation, (2) non-tumor tissue segmentation, (3) cell nuclei segmentation. Core Results: The results suggest that the zero-shot SAM model achieves remarkable segmentation performance for large connected objects. However, it does not consistently achieve satisfying performance for dense instance object segmentation, even with 20 prompts (clicks/boxes) on each image. We also summarized the identified limitations for digital pathology: (1) image resolution, (2) multiple scales, (3) prompt selection, and (4) model fine-tuning. In the future, the few-shot fine-tuning with images from downstream pathological segmentation tasks might help the model to achieve better performance in dense object segmentation.