I have a shallow well jet pump with an old galvanized tank. I've primed the pump and started the pump up. There is no pressure at first. I pull the supply line from the well up and down and pump water into the pump. The pressure goes up to 60 psi. My supply line has water. The pump was set at 50 psi and does not shut off. When I disconnect the power, the pressure drops to 0 psi instantly. I have checked for leaks. Can not find any. Any suggestions? Could it be a bad tank?

The check value is stuck open. Replace value

I agree! If you have found no leaks in the suction line then the check/foot valve must be at fault.
Replace it and let us know if you hold pressure now. Good luck, Tom