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In this paper a method using local moments is proposed for watermarking 3D shapes modelled by mesh surfaces. The moments are used for separating two regions in selected areas. Two different approaches are adopted for 3D shape watermarking, according to the boundary surface between the two regions: by using parallel planes and bounding ellipsoids, respectively. The proposed algorithms change locations of 3D vertices by placing them in one of the two regions, according to a given code. Both algorithms use a vertex selection procedure followed by the embedding. The paper provides a statistical analysis of distortions caused in shapes by geometrical perturbations. Experimental results are provided for various 3D graphical objects.