Deep implicit functions (DIFs) have emerged as a powerful paradigm for many computer vision tasks such as 3D shape reconstruction, generation, registration, completion, editing, and understanding. However, given a set of 3D shapes with associated covariates there is at present no shape representation method which allows to precisely represent the shapes while capturing the individual dependencies on each covariate. Such a method would be of high utility to researchers to discover knowledge hidden in a population of shapes. We propose a 3D Neural Additive Model for Interpretable Shape Representation (NAISR) which describes individual shapes by deforming a shape atlas in accordance to the effect of disentangled covariates. Our approach captures shape population trends and allows for patient-specific predictions through shape transfer. NAISR is the first approach to combine the benefits of deep implicit shape representations with an atlas deforming according to specified covariates. Although our driving problem is the construction of an airway atlas, NAISR is a general approach for modeling, representing, and investigating shape populations. We evaluate NAISR with respect to shape reconstruction, shape disentanglement, shape evolution, and shape transfer for the pediatric upper airway. Our experiments demonstrate that NAISR achieves competitive shape reconstruction performance while retaining interpretability.