Today’s definition of popping a cherry means losing one’s virginity. For that the accepted way to do that by definition is a males' penis must enter the females’ vagina.
If this is your question; then the answer is no; you cannot do so through masturbation.
If you are asking can you rupture your Hymen through masturbation? Then the answer can be yes depending how you masturbate and if you use your fingers or anything else to penetrate your vagina.
Dragonflymagic answered Tuesday March 3 2015, 10:23 pm: There is nothing to pop. There is a skin that for the majority of females is smaller in diameter than circumference of the vagina inside, it's a membrane of skin around the outer edges, and it is stretchy like elastic. It does not cover all the way across or there would be no way for your period fluids to leave your body once a month. I know of someone who used a good visual for this, using a toilet paper roll with a nylon stocking stretched over one end and used scissors to cut a smaller hole in the middle of the circle of stocking. It's called a hymen(the proper word for this membrane) The hymen along the edges will stretch slowly like a rubber band, to fit tampons, sex toys and a penis. One finger likely wouldn't stretch it but if you placed several fingers in to try to stretch it you probably would. Masturbating generaly wont stretch it or tear it. A vibrator or dildo can. The idea that a female must bleed if the hymen is broken by sex is not based in fact at all. Some females are born with a looser hymen, others with a tighter one. What can happen is if no lube is used and a toy or a penis is shoved in fast, there can be tearing and some drops of blood. Using fingers on yourself if nails are rough, can scratch you inside and maybe produce a couple drops of blood. But the hymen and vagina heal just fine on their own and do not need a Dr. unless you have a septate hymen. This would be a strip of membrane crossing from top to bottom in the middle, creating two smaller entrances. Your period can still flow out but something as small as a tampon may be too painful to insert and the male penis can not find its way in at all. In this case, a Dr. will snip that skin away and all with be normal. [ Dragonflymagic's advice column | Ask Dragonflymagic A Question ]
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