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3D mesh models are now widely available for use in various applications. The demand for automatic model analysis and understanding is ever increasing. Mesh segmentation is an important step towards model understanding, and acts as a useful tool for different mesh processing applications, e.g. reverse engineering and modeling by example. We extend a random walk method used previously for image segmentation to give algorithms for both interactive and automatic mesh segmentation. This method is extremely efficient, and scales almost linearly with increasing number of faces. For models of moderate size, interactive performance is achieved with commodity PCs. It is easy-to-implement, robust to noise in the mesh, and yields results suitable for downstream applications for both graphical and engineering models.