Is it normal for an 18 year old girl to be underweight but eating all the time?

No, it is not normal.
It is very possible that you have tapeworms or a thyroid condition. You really need to see a doctor. The sudden drop in weight and the appetite issues indicate to me strongly that you may have a health condition worth investigating.

Medical overdue.

Something is amiss. I would recommend eating organic garlic in ur diet as a natural cure for any tapeworms, plus eat as much organic fruits and veggies as possible for ur health in general. Like spinach, carrots, black beans, sweet potatoe, green tea, and the largest variety of different veggies. You will feel a lot bettrr after this but if ur not better youll have to go to the doc. Oh and cut out ALL hfcs, processed foods and non organic meat.

Dude! Who gives a damn if its normal or not?! Enjoy every second of it!! It's a blessing to eat so much and not get fat. 98% of women envy you for that. Enjoy it while it lasts, when you hit your mid 20's, trust me this won't be a problem!!
Xxx
P.s. If it's "unhealthy" kinda underweight, go to a doctor.

Are you husky or portly?

sound like me. I should be obese, the way I eat. metabolism, yo.

Worms

These are all really good suggestions so far... I second cupcake_wants suggestion about eating healthy and raw foods and staying away from junk and processed foods. The bottom line is that ANY sudden, unexplained loss OR gain of weight should be followed up by a visit to the doctor, no exceptions.

You might have a high metabolism, you are growing or worms in your belly.

It's not normal. It could be cause by many different things like: parasites, extremely fast metabolism (but somehow I don't think that is the case here), Overactive Thyroid, etc. Go to a doctor and have him run some tests on you. Good Luck!

Sweetie, get your doctor to check you gall bladder and liver function. My girlfriend has some sort of blockage in her gall bladder and cannot put on weight. She is stuck on 38kg. On top of that she is a picky eater. I have to constantly monitor her eating and if a disk isn't to her liking, I toss it out and quickly buy another dish before the aroma of food makes her full (eating out is very cheap, average $1.50ea per meal).

I was going to say normal until I re-read and saw that you suddenly dropped so much weight.
I'm pretty sure you got the answer you were looking for from Neuro.
My girlfriend had been underweight her entire life until she got pregnant and gave birth and now she's still very skinny but has curves now. In that case I believe it's normal and healthy in fact.
In your case, it seems to me that you should see a doc. As previously stated.
=] I know I gave a semi-useless comment, but it can be considered 'back-up' to Neuros comment..

Could be coeliac disease, any of the suggestions Neuro made or something else. A sudden loss of weight is not normal though, and you should see a doctor.