No, it should not be collapsed. When hot the pressure builds up in the cooling system and this lifts the spring on the expansion tank cap. The pressure exits via the small pipe by the cap. When it cools the pressure drops and a vacuum is formed which draws air back in - or coolant if there is an overflow bottle attached.
Check the overflow pipe for blockage from the tank to the outlet. It could also be a faulty tank cap or the top hose has lost its resistance and become weak. If the pipe is easily squashed and feels soft, I'd replace it.