Peonies with heavy blooms often need staking. I buy linking stakes and set them into the ground a few inches away from the stalks, encircling the plant. They link well below the flower heads, so the leaves can cover them. That helps keep the plant from falling all the way to the ground, but in a heavy rain the flowers still flop way over. I also have a few stakes that I use singly - they have loops at the top with room to pass a stem through. They support single stems and hold the flower upright. I don't stake all the stems, just a few of the biggest ones. I'm sure other people have different staking methods.