Fill up proble not just the cost

2002 Hyundai Accent. I have trouble filling gas tank. It just started it takes a gallon or two the shuts off. I have to keep restarting to fill tank. This can take up to ten minutes to fill the tank. Can I fix this with out removing the gas tank

You most likely have a problem with the Evaporative Emissions System.
This could be as a result of a few possible issues:

A bad valve solenoid in one of the evap hoses
A kinked evap hose
A contaminated carbon canister, which results from overfilling the tank.
If you have been in the habit of continuing to force gas into the tank after the pump clicks off, then you have essentially killed that expensive carbon canister.
A spider nest in one of the evap hoses. For reasons that I don’t understand, Hyundais seem to be more prone to this spider problem than most other makes.

The only good news is that you probably won’t have to drop the tank!

Depending on how fast the pump is putting out fuel, it’s happened to me. Don’t put the nozzle quite as far in, and pump slightly slower. You may have to hold the handle, instead of locking it full open and just waiting. Try a different station, or at least a different pump and see if the fuel delivery is slower…and if it helps.

One additional possibility - Have you or another driver topped off the tank after the first time it shut off? On many cars if you top off the tank (may take several times) you can damage it.

Actually, Joseph, I did mention that as the third item in my list, above.