Highly therapeutic for our pets as well as ourselves, and 100% safe, there are schools of massage or you can read and practice. Many of the Overview bookslinkalso speak about massage.
The Healing Touch by famous Dr. Michael Fox is a great practical guide.
Canine Massage by Shari Seymour
The Dog Lover’s Guide to Massage: What Your Dog Wants You to Know (and one for Horse, too) by Megan Ayrault LMP