Most runners I see pull their elbows back, behind the rib cage; they seem to “hold” their forearms stiff and elbows up high, swinging this bent structure strictly forward-and-back. This pattern coincides with a tendency to push the chest forward, which restricts easy breathing, and correlates with stiffness in the arms, shoulders, base of the neck, and back.
In standing, the arms ideally hang more forward than the back of the ribs, shown by the far right example of this image. You can see that in the middle “military” style posture, the chest is pushed forward and the elbows are drawn back. In the balanced posture, there’s no pushing forward in the ribs, and the elbows drape alongside the torso.
Rather than pulling my elbows backwards when I run, I think about them releasing forward. I find it informative and helpful to think of myself as being a four-legged creature who just happens to be standing on two legs. This enables me to step out of my habitual ways of standing and moving, and provides insights about the mechanics of the body.
In accordance with what I know about arm movement, I also think about letting my shoulder blades provide support for the forward reach of my arms. You can see in the running cheetah that the shoulder blades move forward as the front legs stretch out in extension. Rather than hold my shoulder blades glued to the back of my torso, and moving bent arms as if they swung solely from the humeral joint, I let my scapulae glide forward with each swing of my arms. With my hands and arms relaxed, it feels a bit like pawing the air! But anyone who has clambered up a mountainside knows what it is to use your arms and legs together; we just sometimes forget that the arms remain active, even when they don’t have contact with the ground. Thinking of running as a four-limbed activity creates a smoother gait and prevents stiffness.