But indestructible it is not.
Fans of ABC's "Grey's Anatomy" got a peek at this possibility when the character of Dr. Mark Sloan "fractured" his penis during sex. Within hours, "penile fracture" and "broken penis" topped Google's most popular search terms.
Fractures - in which penis tissue ruptures like a burst tire - occur more often than one might think. "We usually see a fractured penis every month at our hospitals," says Dr. Tom Lue, professor of urology at UC San Francisco. Even more common, though, are mild, painless injuries to the penis during sex. Such wear and tear can lead to an increasingly prevalent condition known as Peyronie's disease, which leaves the penis with a dramatic bend.
Both conditions are as old as sex itself and documented as far back as the 10th century. But during the last decade a new factor has emerged that may be linked to more complaints of penile trauma: erectile dysfunction medications such as Viagra, Cialis and Levitra.
Experts say these drugs help protect some men from injuries during sex - but put others at greater risk.
When a man becomes aroused, rapidly pumping blood gets trapped in his penis. Two spongy tubes that run through the shaft swell and strain against the surrounding stretchy sheath - known as the tunica albuginea, or "white tunic."
As the penis thickens and lengthens, its elastic tunic expands and thins. But if the tunic stretches beyond a certain point -- as the shaft suddenly flexes too far, for instance - the layers can rip, releasing a small surge of blood. "There will be a sudden blowout," Montague says. "It's usually at the base of the penis, and it's very dramatic."
Doctors call this a fracture (despite the lack of bones in the penis). It is usually accompanied by a popping sound, then swelling and discoloration of the penis to a deep purple hue. Usually, the erection fades and pain sets in (though some couples reportedly try to continue with sex). Men may later find it impossible to urinate.
Young men are most at risk, in part because of the firmness of their erections and athleticism of their activities. Certain sexual positions are more perilous than others. "When a woman is on top, that's a dangerous situation," Lue says. If she bends too far forward or backward, she can create excessive torque on the penis.
Also risky is rear-entry vaginal intercourse because, again, the penis is more likely to bend too far at its base. According to a report published in December in the British Journal of Urology International, this sexual position accounted for half of the penile fractures treated at Brookdale University Hospital in New York between 2003 and 2007.
Careless insertion of the penis can spark a mishap in any position. Men, or their partners, should manually guide the shaft during entry to avoid colliding with a partner's nearby pubic bone, Montague says.
Occasionally, Viagra or related medications are associated with penile fractures. A 2002 case study from India, for instance, described a three-week period in which six men arrived at an emergency room with fractured penises - all resulting from recreational use of sildenafil, the drug sold as Viagra, to achieve, the authors wrote, "prolonged sexual enjoyment, out of curiosity."
Medical reports have also discussed cases resulting from men attempting to fold an erect penis into tight underwear, or rolling onto their stomachs while asleep with nocturnal erections. And then there are odd habits.
In some Middle East regions, men engage in a practice known as taqaandan ("to click" in Kurdish), explains Dr. Javaad Zargooshi, urology professor at Kermanshah University of Medical Sciences in Iran. It's a painless process, similar to knuckle-cracking, in which the top half of an erect penis is bent forcefully while the rest of the shaft is held stationary.
Usually this produces only a loss of erection and a satisfying popping noise, says Zargooshi, who published a report on the phenomenon in December in the Journal of Sexual Medicine. Other times, it will fracture the penis. Taqaandan is a public health concern in western Iran, where penile fractures are unusually common. "The practice of taqaandan is increasing, and we don't know why," Zargooshi says.