The military does not try to eliminate fear but rather attempts to train you to work through the fear. Fear causes normal and predictable reactions in all of us. Knowing what these reactions are combined with constant muscle memory drills allows a person to cope with the fear rather than be crippled by it.
If you are really interested, check out a book called "on killing" written by an American colonel (grossman) If I recal correctly. Extensive research was done on the subject. I didnt read the book myself, but I had to attend his seminar on a few occasions.