Have a 3/4 hp pump with a 25 gallon tank. Pipes go down about thirty feet. This past Saturday it rained very much, later that day the breaker to water pump was tripped. I reset the breaker but a short time later it trips again. Unsure if it's the pump or the underground cable that leads from the house to the pump. Thanks.

No way to tell without pulling out the pump unless there is a point where you can disconnect the power line just before it goes down into the well. If there is then disconnect and reset the breaker. If it pops then likely the breaker itself has gone bad. Is this a GFCI ?

It could be a weak breaker or a dragging pump. I would think the breaker would trip immediately with a wire.

If you have buried cable, it could be a cable problem. Try disconnecting the power from the switch with the breaker off. With the wires off the switch and separated from each other, turn the power back on. If the breaker continues to throw, then the cable is the problem. If the breaker does not throw, then it is more likely you have a pump problem.