Hello Cathryn,
From your description I conclude that you have a water system that is controlled by a pressure switch.
If the pump keeps cycling, then it means that the presure in the pipework is continually decaying.This means that somewhere there is a leak.
Now if none of your taps are dripping, and there are noother visibledrips on the pipe work or joints, then my suspicion falls on the pressure switch.
On the inlet side of the pressure switch is a non return valve. This is designed to lock the pressure in the pipe work, but if the seal in the valve is weeping, this will allow some of the high pressure water to leak back to the pump and water container.
With this condition, there is no visible leak, but as the pressure drops the pump cycles to re set the pressure switch.
Often the cause of this is a water filter cartridge that has started to release carbon granules, which then travel to the non-return valve and jam in the seat.
The valve can be stripped an cleaned, but if the seal is damaged the assembly will need to be replaced.