The most likely cause is contamination of the carbon canister that is the heart of the car’s evaporative emissions system.
The most frequent cause of carbon canister contamination is filling the tank after the gas station’s pump has shut off for the first time. If you are one of those “click, click, click–let’s keep forcing gas into the tank” folks, then you have caused this damage yourself from too many incidents of overfilling the tank.
If the carbon canister is indeed contaminated, it could cost somewhere in the neighborhood of $300 to replace that part.
On the other hand, you could have a spider nest in the evaporative emissions lines. While Hyundais seem to be particularly prone to this situation, it can happen on any car. The solution in this case is to have the evap lines blown out with compressed air, after detaching them at both ends. For your sake, I hope that you have a spider nest problem, rather than a carbon canister problem.