We propose USTNet, a novel deep learning approach designed for learning shape-to-shape translation from unpaired domains in an unsupervised manner. The core of our approach lies in disentangled representation learning that factors out the discriminative features of 3D shapes into content and style codes. Given input shapes from multiple domains, USTNet disentangles their representation into style codes that contain distinctive traits across domains and content codes that contain domain-invariant traits. By fusing the style and content codes of the target and source shapes, our method enables us to synthesize new shapes that resemble the target style and retain the content features of source shapes. Based on the shared style space, our method facilitates shape interpolation by manipulating the style attributes from different domains. Furthermore, by extending the basic building blocks of our network from two-class to multi-class classification, we adapt USTNet to tackle multi-domain shape-to-shape translation. Experimental results show that our approach can generate realistic and natural translated shapes and that our method leads to improved quantitative evaluation metric results compared to 3DSNet.