What kind of animal? It makes a difference whether the animal picking through your trash is a mouse, a rat, a gull, a starling, a raccoon, a dog, an opossum, or a black bear.
The best method for keeping trash cans from being disturbed is to put them inside a secure structure. While it is possible that animals will damage the rubber at the base of your garage door trying to get in, this is unlikely as the animal must: 1) smell the food and 2) dig at that spot.
You can also install an outdoor shed and put the cans in there. An ideal solution (not always possible) is to keep your trash indoors until the day of your scheduled trash pick-up. Most animals are visiting unsecured trash cans at night, so keep the trash indoors solves this problem.
Another way to stop the problem is to secure the lids to the cans with bungee cords or wire. Then anchor the cans to a pole or box so that they cannot be knocked over. Metal cans are preferable to plastic as metal is more resistant to gnawing damage. Additional methods would be to reduce the amount of food garbage in the cans by using a garbage disposal.
Some people have found success spraying ammonia or other strong-smelling product over the trash to help mask the smell. (BE CAREFUL WITH AMMONIA AND NEVER MIX AMMONIA WITH BLEACH!!). However, animals are smart, and you could "educate" them to associate certain smells with food.
You may find that the animals will persist for a while until they discover that they can’t get to the food. So prepare yourself for activity and possibly damage, to increase in the short term.
If damage persists, you may need to think about eliminating the problem with traps set and used in accordance with state law. Remember, however, that this would probably be a short-term solution.
You've probably heard about black bears breaking into cars and tents to get food in National Parks. In black bear country, many parks have "bear-proof" containers. You probably don't need a bear-proof container, but this example is a reminder that an engineering solution certainly is possible. For wildlife, contact your local Extension office or state wildlife agency for additional information. If dogs or cats are getting into your garbage, contact your local animal control agency.
To learn more, you can visit The Internet Center for Wildlife Damage Management