From the title of this post, you might think I am asking you literally to run carrying delicate eggs, but that is not the case. I simply want you to pretend you’re holding an egg in each hand, gently cupping your palm instead of clenching your fists. Rest your thumbs against your fingers and pretend you’re protecting an egg, being careful not

to crush it. This trick should help you relax your grip, which will in turn help relax the muscles in your arms, shoulders, and neck. Releasing tension in your upper body will prevent pain during and after a run. Running is hard enough without the unnecessary tension. Source

Read more here:
Running Tip: Run With an Egg