Mobile robot navigation through natural terrains is a challenging issue with applications such as planetary exploration or search and rescue. This paper proposes navigability assessment of natural terrains scanned from ground-based 3D laser rangefinders. A continuous model of the terrain is obtained as a fuzzy elevation map (FEM). Based on this model, the proposed solution incorporates terrain navigability both in terms of uncertainties of the 3D input data and slope of the fuzzy surface. Moreover, the paper discusses the application of this method for local path planning. For this purpose, the Bug algorithm has been adapted to compute local paths on the navigable region of the FEM. The method has been applied to actual 3D point clouds on two different experimental sites.