Elam, a 17-year veteran and one of the league's most accurate kickers, missed only two kicks last season, his first with the Falcons. But he struggled this year, making only 8-of-15 field-goal attempts from at least 30 yards.
Matt Bryant was signed to replace Elam, who played his first 15 seasons with the Denver Broncos.
The Falcons also released long snapper Bryan Pittman and signed Joe Zelenka to replace him.
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