Seven hospital staff have been suspended for their part in the game, played in mid August.
The game involves being pictured lying down with arms by your side and toes pointing towards the floor.
A hospital official said: "Disciplinary hearings are yet to take place and we cannot predict the outcome."
The images, since removed, were posted on the social networking site Facebook under the title Secret Swindon Emergency Department Group.
Great Western Hospital medical director Dr Alf Troughton said: "A number of staff were suspended following allegations of unprofessional conduct while on night shift duty in the hospital during a weekend in August.
"This did not involve patients and we are satisfied that at no time was patient care compromised.
"The Great Western Hospital sets high standards for staff behaviour at all times and therefore takes any such breaches extremely seriously.
"The allegations have been thoroughly investigated and seven members of staff remain suspended pending formal disciplinary hearings."
A little harsh wouldn't you say?