Absolutely! After the shredded beef is cooked and cooled, it can be frozen in portions in freezer bags or air-tight containers. Pour some of the cooking juices over the top of the beef though before you freeze it. The juices will help prevent the beef from drying and getting freezer burn while stored in the freezer. Shredded beef can be stored for up to a week in the fridge, or up to three months in the freezer.