Flexible grids are used in many Geoscience applications because they can accurately adapt to the great diversity of shapes encountered in nature. These grids raise a number di cult challenges, in particular for fast volume visualization. We propose a generic incremental slicing algorithm for versatile visualization of unstructured grids, these being constituted of arbitary convex cells. The tradeo between the complexity of the grid and the e ciency of the method is addressed by special-purpose data structures and customizations. A general structure based on oriented edges is defined to address the general case. When only a limited number of polyhedron types are present in the grid (zoo grids), memory usage and rendering time are reduced by using a catalog of cell types generated automatically. This data structure is further optimized to deal with stratigraphic grids made of hexahedral cells. The visualization method is applied to several gridded subsurface models conforming to geological structures.