Advances in materials and mechanics designs have led to the development of flexible electronics, which have important applications to human healthcare due to their good biocompatibility and conformal integration with biological tissue. Material innovation and mechanics design have played a key role in designing the substrates and encapsulations of flexible electronics for various bio-integrated systems. This review first introduces the inorganic materials and novel organic materials used for the substrates and encapsulation of flexible electronics, and summarizes their mechanics properties, permeability and optical transmission properties. The structural designs of the substrates are then introduced to ensure the reliability of flexible electronics, including the patterned and pre-strained designs to improve the stretchability, and the strain-isolation and -limiting substrates to reduce the deformation. Some emerging encapsulations are presented to protect the flexible electronics from degradation, environmental erosion or contamination, though they may slightly reduce the stretchability of flexible electronics.