I've never given much practice to this style but recently I discovered its actually a very good style to use and learn. I was forced to use it due to a lack of space, and underhand doesn't require as much space around you as compared to the other styles. With proper hip movement and an underhand release  between the vertical and horizontal axis of your body, you can get some really good shots that are quite powerful.  Not as powerful on short distances as overhand or sidearm shots but still plenty powerful.  I feel a lot more accurate with it on flat ground. I highy recommend to learn some proper underhand, it's a really fun challenge to try and get powerful shots out of this style on short distances, and it feels good for the body. You can really let the projectiles skim the ground.

Underarm is good for distance accurracy,  just keep it down the middle and adjust weight of throw for distance.

Under hand is the easiest to teach to 4-7 year old kids, too.

also good for playing sling catch :)

I think it might feel a little counter intuitive but if you’ve ever seen fast pitch softball pitchers the motion clearly has potential. Seems like a fairly short sling could work with a softball pitch, might be pretty good in that sense.

The majority of the ladies at the competition in Mallorca were using underhand. They weren't half bad with it either. Most were more accurate than me (which isn't saying much but still...). I haven't put much practice into it, but maybe I should. This is a good reminder :D

Don't see why it would not work as well as any other style. 

Definitely a good technique for young kids

While slinging underhand, move the hips like golf players do.

Beginners often first use underhand, but they tend to swing their whole arm instead of just the wrist and throw very vertical instead of that middle point between the horizonal and the vertical.

You could also describe the style I am talking about as a very down-angled sidearm

     Underarm is my most accurate style.  It puts a frontspin on your projectile instead of a backspin like overarm styles do.  This gives it more of a ground hugging trajectory.  It will also cause your projectile to bounce forward and low instead of more straight up as backspin will do.

Rat Man wrote on May 19^th, 2020 at 7:40pm:

Underarm is my most accurate style.  It puts a frontspin on your projectile instead of a backspin like overarm styles do.  This gives it more of a ground hugging trajectory.  It will also cause your projectile to bounce forward and low instead of more straight up as backspin will do.

Yes, I have the same experience.

Under arm is really good for skipping rocks on water.  You'll need a sling that can open on the down stroke, so not too long.  It's going to be height dependent.

Can’t beat it for lobbing big odd shaped chunky rocks into water to make splashes.