I just got a Hyundai Elantra 2002. I have tried filling the tank but can't get much in. Every couple of seconds it shuts off. Takes me 5 minutes to get 2.5 gallons in. The nozzle won't ggo all the way in as well.

The emmissions evaporator cannister needs to be replaced. The charcole elements inside that cannister have finally expired from use through the years

try different positions with nozzle not to far in somewhere near the middle

If there is a rubberized hose (and there probably is) connecting the fill pipe to the tank, check to make sure it hasn't partially collapsed, thereby restricting fuel flow thru it.

I know you probably won't like my answer, but seeing as I am a service tech for gas stations, the nozzle has a safety feature which shuts/kicks off when gas splashes back into the nozzle, thus keeping the gas from running over when the car is unattended and nozzle is locked. You can try pulling the nozzle back til it is barely in the tank or try a different gas station as some nozzles are different. As it is the shape of the fill tube on your vehicle. Hope this helped Tim

Stop and talk to a dealer to see if they have a TSB on this problem,
Dodge had this problem and they corrected it by installing new tanks.

have emission system checked or buy manual and perform test

There is a breather tube fitted to the tank which allows air to escape when you fill it with fuel.

That is either blocked or compressed.

When you take the filler cap off is there a gust of air in or out of the tank

I had this problem on an old Civic I used to have.  Pull the nozzle out one to two inches and try again.  That should do it.  Always worked for me.  Just make sure you don't pull it out too far and spray gas everywhere.  Man I remember what a pain that was too!

possible cause could be evap canister full of gas causing back up

You have a blocked or restricted evaporative cannister or vent valve or both. When you fill the tank with gas, the air is expelled through a line attatched to the emissions cannister and then through another line to the vent valve. If these are restricted or damaged, this could cause your symptoms. Usually you can still fill the tank very slowly though. Usually, the canister ges saturated from gas from overfilling (topping off).
The fix is to replace the EVAP canister.