Many backpacks have side netting as well as compression straps-- use them! They will easily and securely hold a sheathed axe up 28" long. For example, here's a 26" Hudson Bay Axe strapped to a Gregory Denali Pro 105 Pack:
If your axe doesn't have a sheath this obviously won't work as the axe bit will just tear the netting. Also, make sure to counterbalance the weight in your pack on the opposite side of the axe when doing this.
About the author
Jason Schwartz is the founder and senior editor of Rocky Mountain Bushcraft. He is a former Red Cross certified Wilderness & Remote First Aid Instructor, and has taught bushcraft and wilderness survival techniques to the Boy Scouts of America, interned with the US Forest Service, and studied wilderness survival, forestry and wildland firefighting at Colorado Mountain College in Leadville, Colorado. Jason has also written for magazines such as The New Pioneer and Backpacker, including writing the "Tinder Finder" portion of Backpacker's "Complete Guide to Fire," which won a 2015 National Magazine Award (NMA). Email him at rockymountainbushcraft @ hotmail.com (without spaces)