In the current issue of "Classical Fighting Arts" there is an article about this posture.
The image above is from the Uechi Kyohon - however the image in the text a nearly identical illustration. The elbow "strike" being the "flag" that is raised and the other hand (that in Uechi is doing a circle) is the hand that is beating the drum. So one goes up and out and the other goes down and in.
It is called the "flag and drum posture" in the text.
The article is "General Chi'i and the Roots of the Channan Kata" by Henning Wittwer.
Channan being a name for a group of particular Chinese forms related to the modern Okinawan series known as Heian. In the article it is stated that Itosu Tasutsune may have developed the five Heian katas based on a text of the old Channan kata. The supposed author of the text containing the Chinese forms is Ch'i Chi-kuang a general in the in 16th century. The text entitled Chi-hsiao Hsin-shu (The New Treatise on the Disciplined Service) is a manual for training soliders in various forms of combat. Chapter 14 of the text contains drawings of empty handed techniques with three basic themes a)boxing, b) wresting, and c) grappling.
Now that you've got the context, back to the stance.
The author's translation of the notes written near the illustration of the above posture reads:
"The Flag and Drum Position: While pushing forward left and right, give a side-wards strike with one hand when you are close, and squeeze with the other hand to throw him. The people know and benefit and for the seized head of the tiger there is no gate to flee."
Which I would put into more normal english as:
"If your attacker is pushing/shoving forward with both hands and you are in close, strike sideways to the outside of their arm and pull the opposite direction with your other hand to throw him. Everyone knows that where the head goes the body will follow - so that if you catch his momentum moving forward it will be very easy to throw him and very difficult for him to avoid getting thrown."
So you wouldn't be using the elbow so much as a strike in this situation but as a lever/fulcrum. As you step a bit off the line of the push and drop your weight and pull with that circle blocking hand while you bury your elbow into the shover's arm you turn their linear force into a circular throw.