Yes / Physics-based skin deformation methods can greatly improve the realism of character animation, but require non-trivial training, intensive manual intervention, and heavy numerical calculations. Due to these limitations, it is generally time-consuming to implement them, and difficult to achieve a high runtime efficiency. In order to tackle the above limitations caused by numerical calculations of physics-based skin deformation, we propose a simple and efficient analytical approach for physics-based skin deformations. Specifically, we (1) employ Fourier series to convert 3D mesh models into continuous parametric representations through a conversion algorithm, which largely reduces data size and computing time but still keeps high realism, (2) introduce a partial differential equation (PDE)-based skin deformation model and successfully obtain the first analytical solution to physics-based skin deformations which overcomes the limitations of numerical calculations. Our approach is easy to use, highly efficient, and capable to create physically realistic skin deformations. / This research is supported by the PDE-GIR project which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement (No.778035), the National Natural Science Foundation of China (Grant No.51475394), and Innovate UK (Knowledge Transfer Partnerships KTP.010860). Shaojun Bian is also supported by Chinese Scholar Council. Xiaogang Jin is supported by the Key Research and Development Program of Zhejiang Province (No.2018C01090) and the National Natural Science Foundation of China (No.61732015).