Assembly retrieval is a significant technology to reuse the abundant design knowledge embedded in the products. However, the existing assembly retrieval methods are still lacking and the research on this topic is needed. It is found that the motion features of the internal mechanism in the assembly model are closely related to its mechanical function, which is significant for mechanism motion design, assembly simulation, etc. So we propose an approach for assembly matching by motion and shape features. First, assembly model are decomposed into separate kinematic components according to analyzing its motion structure. Then, we take geometric information of kinematic component as a vertex, and kinematic pair between components is taken as an edge to construct graph-based assembly descriptor, which contains motion features of the assembly. Afterwards, Ullmann algorithm is introduced to match the input descriptor with the assemblies in the library, and the maximum subgraph of them is solved so as to estimate the similarity. In case study, some experiments have been carried out, and the results have shown the feasibility of the method proposed in this paper and demonstrated the practical value in engineering.