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In this paper, we consider 3D shape descriptors generated by using functions on a sphere. A set of rotation invariant descriptor vectors is extracted by using spherical harmonics. We first normalize the size of the models, then sample the data from the 3D model surface, and convert the 3D models into point cloud data. We define a unit spherical function for each point on the model surface, and apply spherical harmonics to each function to obtain rotation invariant descriptors. The major contribution of our work is that we can locate a set of rotation invariant descriptor vectors. Moreover, the method is stable to noise on the model surface. Experimental results show that the proposed method performs well in 3D model similarity matching.