31st Regiment
- 31 (City of London) Signal Regiment
- 31 Combat Engineer Regiment (The Elgins)
- 31st (Huntingdonshire) Regiment of Foot
- 31st Battalion (disambiguation)
- 31st Brigade (disambiguation)
- 31st Cavalry Regiment (United States)
- 31st Division (disambiguation)
- 31st Group (disambiguation)
- 31st Illinois Volunteer Infantry Regiment
- 31st Infantry Regiment (Thailand)
- 31st Infantry Regiment (United States)
- 31st Infantry Regiment, United States Colored Troops
- 31st Iowa Volunteer Infantry Regiment
- 31st Mechanized Infantry Regiment "Asturias"
- 31st New York Volunteer Infantry Regiment
- 31st Reserve Field Artillery Regiment (Ireland)
- 31st Squadron (disambiguation)
- 31st Wisconsin Volunteer Infantry Regiment