With 46 teams already entered, the Trust is hoping to attract more competitors to the challenge.
Insurance group IAG has entered three teams and made a video calling for other businesses and groups to join.
Corporate lawyer at the firm, Annemarie Waugh, is team captain and said not only was it a great cause, but the winning group would have ultimate bragging rights.
"You know you are going to save a life, so it's quite amazing," she said.
Her team have been training by doing 14km trail runs in thunder and lightning, and some weight training.
"It's such a great cause and the Auckland Westpac Rescue Helicopter is something that we all might need - whether it's your brother or mum or friend, one day it might even be you."
A training session will be held for teams at Eden Park on Sunday from 1pm to 4pm, and all the details of the race can be found on the Rescue Run website.