The Amby website says there are no known cases of SIDS when using a baby hammock.
To date, there has not been one single case of injury or SIDS attributed to our hammock.
The matresses aren't that firm so that they mould around baby, but babies aren't meant to lie on their tummy in the hammock anyway. They have mesh sides so there is plenty of airflow.

If you want to see a hammock set up let me know and I'm happy to show you mine