Dents on the aircraft skin are frequent and may easily go undetected during airworthiness checks, as their inspection process is tedious and extremely subject to human factors and environmental conditions. Nowadays, 3D scanning technologies are being proposed for more reliable, human-independent measurements, yet the process of inspection and reporting remains laborious and time consuming because data acquisition and validation are still carried out by the engineer. For full automation of dent inspection, the acquired point cloud data must be analysed via a reliable segmentation algorithm, releasing humans from the search and evaluation of damage. This paper reports on two developments towards automated dent inspection. The first is a method to generate a synthetic dataset of dented surfaces to train a fully convolutional neural network.The training of machine learning algorithms needs a substantial volume of dent data, which is not readily available. Dents are thus simulated in random positions and shapes, within criteria and definitions of a Boeing 737 structural repair manual. The noise distribution from the scanning apparatus is then added to reflect the complete process of 3D point acquisition on the training. The second proposition is a surface fitting strategy to convert 3D point clouds to 2.5D. This allows higher resolution point clouds to be processed with a small amount of memory compared with state-of-the-art methods involving 3D sampling approaches. Simulations with available ground truth data show that the proposed technique reaches an intersection-over-union of over 80%. Experiments over dent samples prove an effective detection of dents with a speed of over 500 000 points per second.