The men, now 41 and 42, now live in the Salt Lake City area.
The lawsuit claims that Mormon men in their 20s, who qualified for supervisory positions after completing their two-year missions, ran the camps, which recruited minors from church wards and scouting organizations.
The lawsuit claims that one man, who was appointed camp coordinator, branch president and stake high counselor for one of the camps, molested the two boys from 1986 until 1989.
The lawsuit also claims that the defendants knew of the camp coordinator's "pedophilic sexual violence."
Cody Craynor, a spokesman for the LDS church, said, "The Church of Jesus Christ of Latter-day Saints has zero tolerance for abuse of any kind and works actively to prevent abuse. This case was filed yesterday, and many details in the legal complaint are unclear. The church will examine the allegations and respond appropriately."
The alleged victims are seeking unspecified monetary damages, as well as changes to how the LDS Church deals with sexual abuse, and a written apology from the church.
The Maui Land and Pineapple Company Inc. did not immediately return messages left seeking comment.
The lawsuit was made possible by a Hawaii law passed in 2012 that increases the previous two-year time limit to bring sexual assault civil suits to eight years from the time an alleged victim turns 18, or three years from when an alleged victim realizes his or her injury is due to the sexual offense, according to attorneys for the two Utah men.