Shoulder dystocia is a specific case of dystocia whereby after the delivery of the head, the anterior shoulder of the infant cannot pass below the pubic symphysis, or requires significant manipulation to pass below the pubic symphysis. It is diagnosed when the shoulders fail to deliver shortly after the fetal head. In shoulder dystocia, it is the chin that presses against the walls of the perineum
So, the most common way I've seen this handled in the hospital is by using the McRoberts Manuver, which just means pulling your knees all the way back to your ears... followed by suprapubic pressure. The technique is effective in about 42% of cases. Although McRoberts maneuver and suprapubic pressure are generally safe, it is possible to cause maternal injury by performing them.
Personally, I would like to see more of the Gaskin maneuver, named after Certified Professional Midwife, Ina May Gaskin, which involves moving the mother to an all fours position with the back arched, widening the pelvic outlet. I partially understand why it isn't... most women in the hospital have an epidural, and most likely it is heavy enough that quickly moving to an all fours position is nearly impossible.
BUT, for those mothers that can assume this position, the results are good.
One study found:
The most significant observations of the study were the negative findings. No still births or neonatal deaths were reported. Not a single infant suffered Erb palsy, either transient or permanent, and no newborns experienced seizures, hemorrhage, hypoxic-ischemic encephalopathy, cerebral palsy, or fractured clavicle. No patients required any tocolytic medication during labor. No vaginal, cervical, or uterine lacerations occurred. No women required transfusions. And no cases of postpartum, ileus or pulmonary embolus were reported. Overall, the maternal complication associated with the use of the “Gaskin Maneuver” was 1.2 percent (one case of postpartum hemorrhage, transfusion not required), and the neonatal complication rate was 4.9 percent. . . None of these patients required any additional maneuvers. . . Not only was the Gaskin Maneuver instrumental in relieving shoulder impact in every instance, it is also a non-invasive procedure requiring only a change of maternal position.” The average time needed to assume the position and complete the delivery was 2-3 minutes, with the longest reported interval being 6 minutes.