The invention discloses a side displacement restraint device used for a detachable steel rail damping fastener. The side displacement restraint device is of a layered structure and comprises a first stainless steel metal plate and a second stainless steel metal plate which are arranged oppositely on the two sides. The first stainless steel metal plate and a second stainless steel metal plate clampa plurality of sets of rubber thin layers and a plurality of metal thin plates in a staggered mode. The rubber thin layers and the metal thin plates are vulcanized into a whole. The outer side wall of the first stainless steel metal plate is provided with an inclined surface with the inclined degree of 3-5 degrees. The outer side wall of the second stainless steel metal plate is provided with pins. The number of the rubber thin layers is 4-7, and the thickness of the rubber thin layers is 3-5 mm. The number of the metal thin plates is 3-6, and the thickness of the metal plates is 2-4 mm. Theside displacement restraint device is reasonable in structural design, transverse displacement and overturning displacement of an upper pad plate can be strictly controlled while vertical vibration ofthe upper pad plate is not hampered, and relative sliding friction does not exist.