This paper presents an algorithm for the robust watermarking of 3D polygonal mesh models. The proposed algorithm embeds the watermark into a 2D image extracted from the 3D model, rather than directly embedding it into 3D geometry. The proposed embedding domain, i.e., the 2D image, is devised to be robust against the attacks like mesh simplification which severely modifies the vertices and connectivity while preserving the appearance of the model. The watermark-embedded model is obtained by using a simple vertex perturbation algorithm without iterative optimization. Two exemplary watermark applications using the proposed methods are also presented: one is to embed several bits into 3D models and the other is to detect only the existence of a watermark. The experimental results show that the proposed algorithm is robust against similarity transform, mesh simplification, additive Gaussian noise, quantization of vertex coordinates and mesh smoothing, and that its computational complexity is lower than that of the conventional methods.