This could be caused by a number of things:
1) Faulty sender unit (located in the petrol tank)
2) Faulty Wiring
3) Faulty Petrol Gauge (unlikely)
If I were you I would first concentrate on the the wiring.
If the live side of the circuit (+12v) is shorting to earth (0v) this will cause the gauge to read 'FULL'.
If the live side, or earth connection is loose and the circuit is broken, the gauge will read 'EMPTY'.
Have a look at the connections at the sender, and gauge just to make sure they are secure.
If they are secure and the fault is still present, there could be a short somewhere else in the circuit caused by broken insulation on a cable. This will be harder to trace, as it could be anywhere in the car.
If the fault still cannot be found either the sender or the gauge may be faulty. These parts may be expensive.
But as I say look at the wiring first, this is more likely where the fault lies.
Hope this helps. wink
Keep us posted