Oven shows an F2 flashing after self cleaning along with a beeping sound.

Oven keeps beeping:
As there is no reprogramming of most control boards try this, disconnect the power and wait 30 seconds and then reconnecting the power.

If it's an "F1" fault code this generally implies an electronic oven control (EOC) failure. Disconnect the power, wait 30 seconds or longer and then reapply power. If "F1" returns upon power-up, replace the electronic oven control.
The oven control can be accessed and replaced from the rear of the control panel.

NOTE:Disconnect the power cord from the power source before removing the panel from behind the console.
If its an F2 ERROR CODE, The F2 error indicates an open circuit in the oven temperature probe.

Your range has a resettable thermostat in series with the oven temperature probe. If this thermostat opens the clock will display F2 and the oven won't heat.
You can reset the thermostat by pushing in the reset button on top of the thermostat.
Some ovens have an alarm that will beep continuously every six seconds to alert you that the oven is still on. Usually, a kitchen timer that you have set will cause the beeping, but occasionally it can be an error with the oven's settings. If it is the kitchen timer, you can simply push the "Kitchen Timer On/Off" button to end the continuous beeping. If that does not stop the beeping, it is probably beeping due to an error. You can turn the continuous beeping off but you may still need to troubleshoot the issue that is causing the beeping noise.

Read more :
http://www.ehow.com/how_12086370_ge-oven-stop-beeping.html

F2 Oven Temp Exceeds 590 with unlocked door High resistance in Sensor, likely a bad sensor



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F2 Oven cavity thermistor closed Check oven thermistor for continuity. Replace if zero or infinite ohms.

the f2 is telling you that the tempature is to high. It could be your control board. I personely would call a tech as its got to do with the contacts on the control board or the door lock. can be several different problems.

F2 is a bad temp sensor, needs to be replaced.

REPLACE THE OVEN TERMISTER PROB IT WILL FIX YOUR PROBLEM. CALL 800-614-2700 TO GET PRICE ON IT AND HAVE MODLE # REDAY

My oven will not stay on, when started to preheat it will come on for a few seconds and they it will make a beeping noise and the codes E0 F2 will appear. The codes stay on even if the oven is off.

I used the self cleaning mode for 2 hours and the error f2 keeps flashing and beeping, I did try to power off with the breaker and left it off for about a half hour and it still continues to beep and flash f2, what should I do?

what is solution

I have the exact problem, had a service man look at it while still under warranty. He said it was fixed and left. Tried it again, same problem. Called him back 2 times after that, he quit responding to my calls. By tyhen warranty expired and GE refused to do anything.