Barnes, who has been a major player in songwriter circles for the past two decades, died early Sunday at Baptist Hospital, The Tennessean reported Monday.
"Max was one of the greats," said country singing legend Merle Haggard, who recorded and co-wrote numerous songs with Barnes.
Barnes was inducted into the Nashville Songwriters Association International Hall of Fame in 1992. He won song of the year awards from the Country Music Association for Gill's "Look At Us" and Vern Gosdin's "Chiseled In Stone," which also was nominated for a Grammy.
Other Barnes' songwriting hits included Conway Twitty's "Don't Take It Away" and "Redneckin', Love Makin' Night," George Jones' "Who's Gonna Fill Their Shoes," Randy Travis' "Storms Of Life" and Keith Whitley's "Ten Feet Away."
Barnes' son, Max T. Barnes, also is a successful Nashville songwriter.