Additive manufacturing is an arising technology for soft materials and structures with improved complexity and functionality, and it has been gradually widespread in fields including soft robotics, flexible electronics and biomedical devices. Along with the development of material systems and fabrication techniques, mechanical design principles for additive manufactured soft materials were greatly developed and evolved over the past few years, and some special issues that are distinct from conventional manufacturing techniques emerged. In this short review, we mainly focus on additive manufactured soft materials that are in great request of mechanical models/simulations to provide design guidelines, therefore, topics such as soft robotics and electronics are out of scope here. We firstly discuss the mechanical designs for controlling shape distortions and interfacial strength, as they are directly related to the quality and reliability of additive manufactured soft materials. Then, design principles and manufacturing strategies for bio-inspired composites, which makes up a large part of current researches on additive manufactured soft materials, are summarized integrally from three aspects. In addition, basic mechanical considerations for additive manufactured 4D shape changing structures are explained, together with the review of recent theories and numerical approaches. Finally, suggestions and perspectives are given for future developments of soft material additive manufacturing.