Rzepczynski, 32, had a 9.39 ERA and 2.87 WHIP in 18 appearances. He allowed 13 hits and walked nine in just 7 2/3 innings.
"Obviously Zep has struggled," Mariners manager Scott Servais told reporters on Thursday, one day before the roster move. "He is a high ground-ball rate guy and it hasn't been that way much of this season and the balls have been up and a little flatter. It just hasn't worked out that well with him."
The Mariners have seven days to trade, release or outright Rzepczynski to the minor league.
Elias, 29, was reacquired from the Boston Red Sox in April. He is 2-4 with a 4.94 ERA in seven appearances (six starts) at Triple-A Tacoma.
Elias went 10-12 with a 3.85 ERA for the Mariners in 2014. He was traded to Boston following the 2015 season.
Elias is 15-21 with a 4.20 ERA in 55 career major league appearances (50 starts).
Rzepczynski is 14-27 with a 3.92 ERA in 501 career appearances (23 starts). Seattle is his seventh major league team.
--Field Level Media