Abstract: 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. For scientific shape discovery purpose, we propose a 3D Neural Additive Model for Interpretable Shape Representation ($\texttt{NAISR}$) 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. $\texttt{NAISR}$ is the first approach to combine the benefits of deep implicit shape representations with an atlas deforming according to specified covariates. We evaluate $\texttt{NAISR}$ with respect to shape reconstruction, shape disentanglement, shape evolution, and shape transfer on three datasets, i.e. 1) $\textit{Starman}$, a simulated 2D shape dataset; 2) ADNI hippocampus 3D shape dataset; 3) pediatric airway 3D shape dataset. Our experiments demonstrate that $\texttt{NAISR}$ achieves competitive shape reconstruction performance while retaining interpretability. Our code is available at https://github.com/uncbiag/NAISR.