Similarity assessment between 3D models is an important problem in many fields including medicine, biology and industry. As there is no direct method to compare 3D geometries, different model representations (shape signatures) are developed to enable shape description, indexing and clustering. Even though some of those descriptors proved to achieve high classification precision, their application is often limited. In this work, a different approach to similarity assessment of 3D CAD models was presented. Instead of focusing on one specific shape signature, 45 easy-to-extract shape signatures were considered simultaneously. The vector of those features constituted an input for 3 machine learning algorithms: the random forest classifier, the support vector classifier and the fully connected neural network. The usefulness of the proposed approach was evaluated with a dataset consisting of over 1600 CAD models belonging to 9 separate classes. Different values of hyperparameters, as well as neural network configurations, were considered. Retrieval accuracy exceeding 99% was achieved on the test dataset.