Title: Deep Physics-based Deformable Models for Efficient Shape Abstractions. Abstract: Efficient shape abstraction with explainability is challenging due to the complex geometries of natural objects. Recent methods learn to represent objects using a set of simple primitives or fit locally parameterized deformable models to the target shapes. However, these methods either are limited in geometric flexibility or fail to intrinsically offer shape abstractions with explainability. In this paper, we investigate salient and efficient primitive descriptors for accurate shape abstractions, and propose \textit{Deep Physics-based Deformable Model (DPDM)}. DPDM employs global deformations with parameter functions and local deformations. These properties enable DPDM to abstract complex object shapes with significantly fewer primitives that offer broader geometry coverage and finer details. DPDM learning formulation is based on physics-based modeling (i.e., dynamics and kinematics) to enable multiscale explainable abstractions. The proposed DPDM is evaluated on two different shape abstraction tasks: 3D shape reconstruction and object segmentation. Extensive experiments on \textit{ShapeNet} demonstrate that DPDM outperforms the state-of-the-art methods in terms of reconstruction accuracy and is more robust since it uses much fewer primitives. We conduct comprehensive experiments on \textit{ACDC}, \textit{M\&Ms}, and \textit{M\&Ms-2} for cardiac MR segmentation, and show the leading abstraction performance of our approach.