The relaxation characteristics of silicone rubber insulation will reduce the terminal interface pressure of cable, and then deteriorate its dielectric properties, affecting the stable operation of cable. Since the relaxation characteristics are affected by crosslinking behavior, silicone rubber samples with different crosslinking degrees were prepared by adjusting the proportion of vulcanizing agent and catalyst, the stress relaxation characteristics were characterized by various methods, and the interface pressure was predicted from the perspective of mechanical stress and thermal stress. The results show that with the increase of temperature and elongation of silicone rubber, the stress relaxation will be intensified, resulting in the decrease of interfacial mechanical stress and pressure, but the relaxation of molecular chain segments will lead to the increase of thermal expansion coefficient, resulting in increase of thermal stress and interfacial pressure. Properly increasing the crosslinking degree of silicone rubber can enhance its stress relaxation resistance. The study of broadband dielectric spectroscopy shows that there are dielectric relaxation processes δ and α caused by the molecular chain relaxation polarization and dipole chain relaxation polarization of silicone rubber insulation. The increase of crosslinking degree limits the rotational orientation of molecular chains and steering motion of dipole chain segments, and decreases the polarization intensity of the two dielectric relaxation processes. High crosslinking degree gives silicone rubber strong stress relaxation resistance, and it is predicted that the interfacial pressure retention rate can be as high as 90.7% after 30 years, and showing a long storage period. The results can provide reference for the evaluation of the running state and life of silicone rubber insulated cable accessories.