To provide a system capable of shortening a running mesh of a tire chain without troublesome work even in a difficult situation, and simple in operation without causing a failure.

This shortening element includes at least one socket, and chain strands at a lock position 32 can be fixed in the socket to be incapable of displacing with each other in the longitudinal direction thereof. A running mesh 1 is adjusted to various tire diameters without using a tool, the socket includes at least one locking slit 18 and at least one pull-in opening 24, and at least one chain strand 6 at the lock position 32 can be stored in the locking slit 18. The chain strand 6 can be moved in the longitudinal direction with respect to the other chain strand in the pull-in opening 24. Thereby, the running mesh can be shortened by a simple method.