Overhead pressing issues come in two varieties: strength problems or pain problems. Both come down to one thing: position. If you are lacking the adequate shoulder flexion required for locking your arms above your head, three things will happen:
First, make sure that you have a balanced training program. It doesn't take a genius to know that if you're pressing horizontally (bench pressing) all the time and not doing any pulling, then you can stretch all you want but you're not strengthening in a comprehensive way – you're always playing "preventative catch-up."
Next, open your lats up. Try this lat stretch first and see if there's an improvement in your overhead position.
Next up is bridge progressions. Opening up your upper back will not only improve your overhead position but also your ability to keep an upright torso in your squat. Here's everything you need to know about bridging.
If you've tried all of those then you can start to work on loaded stretching. Make sure to have a spotter or record yourself to get a true assessment.
You can then perform some reps:
As for times/reps etc., just do it until you have a noticeable improvement. Always have something to retest afterwards like your overhead press or handstand.
If you're a big muscley dude and this gives you no improvement, you could also include a roller in the stretch to increase your thoracic mobility. I wouldn't recommend the roller if you don't have much muscle on your back: you don't want to compress your spine, and it shouldn't feel like you are while stretching.
Treat this exercise with respect. It's a loaded stretch, not a strength exercise.
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