This paper develops a digital watermarking methodology for 3-D graphical objects defined by polygonal meshes. In watermarking or fingerprinting the aim is to embed a code in a given media without producing identifiable changes to it. One should be able to retrieve the embedded information even after the shape had suffered various modifications. Two blind watermarking techniques applying perturbations onto the local geometry for selected vertices are described in this paper. The proposed methods produce localized changes of vertex locations that do not alter the mesh topology. A study of the effects caused by vertex location modification is provided for a general class of surfaces. The robustness of the proposed algorithms is tested at noise perturbation and object cropping.