Reverse engineering (RE) is a process to create computer aided design (CAD) models from the scanned data of an existing part acquired using 3D position scanners. This paper proposes a novel methodology of extracting geometric features directly from a set of 3D scanned points, which utilizes the concepts of feature-based technology and artificial neural networks (ANNs). The use of ANN has enabled the development of a flexible feature-based RE application that can be trained to deal with various features. The following four main tasks were mainly investigated and implemented: (1) Data reduction; (2) edge detection; (3) ANN-based feature recognition; (4) feature extraction. This approach was validated with a variety of real industrial components. The test results show that the developed feature-based RE application proved to be suitable for reconstructing prismatic features such as block, pocket, step, slot, hole, and boss, which are very common and crucial in mechanical engineering products.