Statistical shape modeling is an important tool to characterize variation in anatomical morphology. Typical shapes of interest are measured using 3D imaging and a subsequent pipeline of registration, segmentation, and some extraction of shape features or projections onto some lower-dimensional shape space, which facilitates subsequent statistical analysis. Many methods for constructing compact shape representations have been proposed, but are often impractical due to the sequence of image preprocessing operations, which involve significant parameter tuning, manual delineation, and/or quality control by the users. We propose DeepSSM: a deep learning approach to extract a low-dimensional shape representation directly from 3D images, requiring virtually no parameter tuning or user assistance. DeepSSM uses a convolutional neural network (CNN) that simultaneously localizes the biological structure of interest, establishes correspondences, and projects these points onto a low-dimensional shape representation in the form of PCA loadings within a point distribution model. To overcome the challenge of the limited availability of training images with dense correspondences, we present a novel data augmentation procedure that uses existing correspondences on a relatively small set of processed images with shape statistics to create plausible training samples with known shape parameters. In this way, we leverage the limited CT/MRI scans (40-50) into thousands of images needed to train a deep neural net. After the training, the CNN automatically produces accurate low-dimensional shape representations for unseen images. We validate DeepSSM for three different applications pertaining to modeling pediatric cranial CT for characterization of metopic craniosynostosis, femur CT scans identifying morphologic deformities of the hip due to femoroacetabular impingement, and left atrium MRI scans for atrial fibrillation recurrence prediction.