Statistical shape modeling (SSM) characterizes anatomical variations in a population of shapes generated from medical images. Statistical analysis of shapes requires consistent shape representation across samples in shape cohort. Establishing this representation entails a processing pipeline that includes anatomy segmentation, image re-sampling, shape-based registration, and non-linear, iterative optimization. These shape representations are then used to extract low-dimensional shape descriptors that are anatomically relevant to facilitate subsequent statistical analyses in different applications. However, the current process of obtaining these shape descriptors from imaging data relies on human and computational resources, requiring domain expertise for segmenting anatomies of interest. Moreover, this same taxing pipeline needs to be repeated to infer shape descriptors for new image data using a pre-trained/existing shape model. Here, we propose DeepSSM, a deep learning-based framework for learning the functional mapping from images to low-dimensional shape descriptors and their associated shape representations, thereby inferring statistical representation of anatomy directly from 3D images. Once trained using an existing shape model, DeepSSM circumvents the heavy and manual pre-processing and segmentation required by classical models and significantly improves the computational time, making it a viable solution for fully end-to-end shape modeling applications. In addition, we introduce a model-based data-augmentation strategy to address data scarcity, a typical scenario in shape modeling applications. Finally, this paper presents and analyzes two different architectural variants of DeepSSM with different loss functions using three medical datasets and their downstream clinical application. Experiments showcase that DeepSSM performs comparably or better to the state-of-the-art SSM both quantitatively and on application-driven downstream tasks. Therefore, DeepSSM aims to provide a comprehensive blueprint for deep learning-based image-to-shape models.