The Pet Policy is simple: pets are allowed to travel with you in the main cabin. Delta Airlines welcomes pets and our passengers on all of its flights. Delta Airlines has a pet policy that allows you to bring your pet with you on all flights. Delta Airlines is one of the best airlines for dogs and cats traveling with their family. The airline allows pets to fly with their family in the Main Cabin, meaning you can fly with your furry friends all around the world! However, there are some conditions that you must follow in order for your dog or cat to travel with you in delta airlines. If it's not clear what these conditions of Delta Airlines Pet Policy are, please contact customer service before traveling by calling.