Manufacturer:
Cannot find any indication on the furnace as to make and model other than a little plaque that reads "Day & Night".

Age of equipment:
~ 18 yrs old

Efficiency:
80%.

Type of system:
Forced air gas furnace.

Type of fuel:
NG

Try to turn furnace off and on at power switch or breaker. Did this do anything?
No.

Thermostat settings:
Fan set to auto. New Honeywell digital thermostat just installed [it was a 4-wire installation] by me as I thought the original thermostat might be the problem. It didn't fix the problem. But it looks nice.:rolleyes:

Problem:
Furnace starts and operates normally. However, when it reaches temperature and goes off, it comes right back on and goes right back off, 3 or 4 times. The first 2 or 3 times are one right after the other, but the fourth one is usually about two seconds after the third.

That's it. Anything anyone can tell me will very appreciated.

Well, don't run away... This sounds to mee like your limit switch. A small silver box mounted on the furnace itself. Usually has a white push-button on it. How long does it stay on when it turns back on ?

Not more than a second.

On.Off.. On.Off.. On.Off... On.Off

Like that.

Thanks.

Do you have a pilot that lights each time you turn on the thermostat? Is it lit with a spark ignitor? Does the pilot have three wires coming from it? If the answers are yes then you have a bi-metal switch at the pilot that heats up and makes a connection in the pilot that switches to the gas valve to come on, if this switch is weak or the pilot is weak this little switch does not get all the heat it needs and the switch will open and close then in just a few seconds it has heated again and will open but for some reason it will close again and cause that cycling. But after several times of this the pilot switch should get hot enough that it will stay on.
If you don't think this is your problem than give us some more clues, we will try to help.

Thank you letmetellu, but I don't think that's it. This happens at the end of a heating cycle, not at the beginning [which is what I think you're describing].

The only other piece of information I can state is that the old thermostat that I replaced was a Robert Shaw thermostat.