The men could be heard on the video saying, "Yeah! We have now modified Goblin Valley... a new Goblin Valley exists."
You can see the men cheering as they knocked over one of the formations in Goblin Valley State Park.
The video was obtained by the Salt Lake Tribune after the men posted it on Facebook.
Park officials say the priceless goblin formation cannot be restored.
Watch the video: http://bit.ly/H2ILZV
KGO-TV San Francisco, CA contributed to this report.