The incident occurred in Croston Road, Lostock Hall, on Friday night (June 4), British Transport Police said.
Officers said the offenders pushed the coping stone off the bridge onto the track below, damaging lineside cables.
Passing trains also clipped the stone which caused damage to the bodywork.
Pictures of the bridge and the stone were released this afternoon (June 6) as part of an appeal for information.
"Anyone with information should please text the BTP on 61016, quoting reference number 2100040267," a spokesman for the BTP said.
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