Hendricks took a no-decision, giving up four runs on five hits in six innings. He walked three and struck out seven.
Beeler gave up four runs over five innings in the Cubs' 4-1 loss to the Reds on Wednesday in his second big league start.
The Cubs have yet to decide how they'll fill the two vacancies in the rotation created by last Friday's trade of Jeff Samardzija and Jason Hammel to the A's. Jake Arrieta, Travis Wood and Edwin Jackson will start the final three games before the All-Star break at Wrigley Field against the Braves.
Hendricks was 10-5 with a 3.59 ERA in 17 starts at Triple-A Iowa. He is one rotation option, as is right-hander Dan Straily, who was acquired in the deal with Oakland.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.