Being able to reuse existing design knowledge is of major interest to help designers during the creation of new products. This is true at the level of the parts and even more at the level of the assemblies of multiple parts. Meaningful information and knowledge can be extracted from existing geometric models and associated data and metadata, as well as from the processes followed to define them. This paper proposes a method to characterize and structure CAD assembly models to enable the retrieving of similar models from a database. A framework has been devised for the retrieval of globally and/or partially similar assembly models according to multiple user-specified search criteria. It is based on an assembly descriptor, called the Enriched Assembly Model, which is an attributed graph that encodes all the required data automatically extracted from the geometry and structure of the CAD models. The data are organized in four layers: structural, assembly interface, shape and statistic layers. Starting from a real CAD model or from an abstract query model, the algorithm retrieves models from the database by solving a matching problem. The matching between two assembly models is translated into the problem of finding a sub-isomorphism between two EAMs. The layered organization of the EAM allows partially defined queries, which can be further refined. The effectiveness of the proposed approach is illustrated with results obtained from the developed software prototype.