Abstract: In this paper, we present an algorithm for partial shape retrieval on a collection of 3D polygonal meshes. The proposed algorithm is invariant against rigid transformations and robust against nonrigid transformations. By using structure properties and geometric properties to represent shapes. Structure property is represented by a Reeb graph which uses an integral geodesic distance as a Morse function, whereas geometric property is represented by a Pose invariant Shape Signature. The main idea is to use Reeb graph for decomposing shape into many meaningful sub parts. Then describing each sub part by the Pose-invariant Shape Signature. The similarity is computed based on the Approximate Maximum Common Subgraph [Marini et al. 2005; Biasotti et al. 2006] for matching each sub-part between query shape and other while preserving topology. We evaluate our algorithm on various different model classes and deformation.