Non-manifold models have classically been used in Finite Element (FE) simulations to describe the shape of a mechanical part. Sketching the shape of an object is also important in a design stage, where non-manifold models could be of help for the designer. The purpose of the taxonomy proposed here is to be able either to accept or reject them based on the design context and on the type of product. This will contribute to model non-manifold objects and to their binary classification. The proposed taxonomy is also based on the topological properties of non-manifold objects, and especially on topological invariants. We will classify several topological properties as local or global ones, and we will illustrate how such properties can help either modelling these objects or searching for them in industrial data bases when large numbers of FE models have been stored.