One no-equipment move fixes shoulder press pain: sit with your chin supported, lift your elbow level with your hand, press outward using your subscapularis, then lower slowly. Do it pain-free with perfect form before adding any weight.
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If you're having pain when you're shoulder pressing, do this one move. It's non-weighted. You don't need any instruments. All you gotta do is find a bench or even the edge of a bed. You're gonna sit down, chin supported, bring your elbow up, rotate the elbow down so that the hand and the elbow are the same height, press out using your subscap muscle, muscles around your shoulder blade, hold, bring it back in nice and slow, and then rotate back down. Once you can do that pain-free with no weight, then you can add maybe 1 to 2 pounds. But make sure that your form is perfect, that elbow and the hand are perfectly symmetrical and flat with the ground, and you will improve your shoulder pressing function by a thousand times. I promise you.