Although you might not recognize it, Upward Facing Dog actually acts as a backbend. Schuyler Grant of Kula Yoga explains that the idea behind Cobra and Up Dog is to "maintain stability in your lower abdomen and lengthen your lower back." When you draw attention to your belly and back, you'll find that bringing the bend to your upper back comes much more naturally.
People tend to hang out in Upward Facing Dog and focus on pushing up through their arms. Underutilizing your legs, chest, and shoulder muscles in Upward Dog is a big mistake, since those are what should be working in the pose. Schuyler gives a helpful tip to visualize the pose once you're moving into it: "Always feel like you're pulling your chest forward and through, not pushing it up away from the floor." Once you make this shift in your practice, you'll find more flexibility (and less tension) between your shoulder blades and in your chest.
Source: Laughing River Yoga