The best replacement for overhead press is bench press.

The best alternatives to overhead press are rated as following:
★★★★★  bench press
★★★  push press
★★★  shoulder press
★★★  military press
★★  dips
★★  military
★  incline press
★  lateral raises
★  bench
★  upright row
★  dumbbell shoulder press
★  handstand push up
★  seated
★  sitting overhead press
★  handstand pushup
★  behind the neck press
★  upright rows
  clean and jerk
  front raise
  db shoulder press
  clean and press

Your alternative for overhead press is not listed? Suggest!
Speaking about overhead press, one probably shouldn't forget about squat.

Other search terms related to overhead press and their ratings are:
★★★★★ squat
shoulder pain
You have in mind a companion for overhead press and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of overhead press in all years. Click on graph for more.
overhead press
bench press
push press