This paper primarily investigates the use of shape-based features by an Automatic Target Recognition (ATR) system to classify various types of targets in Synthetic Aperture Radar (SAR) images. In specific, shapes of target outlines are represented via Elliptical Fourier Descriptors (EFDs), which, in turn, are utilized as recognition features. According to the proposed ATR approach, a segmentation stage first isolates the target region from shadow and ground clutter via a sequence of fast thresholding and morphological operations. Next, a number of EFDs are computed that can sufficiently describe the salient characteristics of the target outline. Finally, a classification stage based on an ensemble of Support Vector Machines identifies the target with the appropriate class label. In order to experimentally illustrate the merit of the proposed approach, SAR intensity images from the well-known Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset were used as 10-class and 3-class recognition problems. Furthermore, comparisons were drawn in terms of classification performance and computational complexity to other successful methods discussed in the literature, such as template matching methods. The obtained results portray that only a very limited amount of EFDs are required to achieve recognition rates that are competitive to well-established approaches.