The meet will take place at the Rose-Hulman Institute of Technology in Terra Haute. Competition will take place on Friday, March 13, and Saturday, March 14.
Gleason qualified in the mile run when he raced to the finish in 4:11.03 on February 20 at the Snow Shoe Open at the University of Minnesota.
The prelims for the mile will take place on Friday at 4:20 p.m. The finals will take place on Saturday at 2:10 p.m.
This weekend's meet will mark Gleason's third nationals appearance in a year. He qualified for the same meet in 2008 and for cross country nationals this past fall.
King will make his debut at nationals in the shot put on Saturday at 3:30 p.m. He qualified with a throw of 16.39 meters (53-9 1/4) on February 7 at the Border Battle at UW-Superior.
The nationals announcement comes after a weekend in which the Pipers finished second of 11 teams at the MIAC indoor conference championship.