The fields of 3D computer vision, 3D robotic perception and photogrammetry rely more and more heavily on matching 3D local descriptors, computed on a small neighborhood of a point cloud or a mesh, to carry out tasks such as point cloud registration, 3D object recognition and pose estimation in clutter, SLAM, 3D object retrieval. One major drawback of these applications is currently the high computational cost of processing 3D point clouds, with the 3D descriptor computation representing one of the main bottlenecks. In this paper we explore the optimization for parallel architectures of the recently proposed SHOT descriptor [22] and of its extension to RGB-D data [23]. Even though some steps of the original algorithm are not directly suitable for parallel optimization, we are able to obtain notable speed-ups with respect to the CPU implementation. We also show an application of our optimization to 3D object recognition in clutter, where the proposed parallel implementation allows for real-time 3D local description.