Some jet pumps will have a built-in check valve. If your pump does not have one, a separate check valve OR a foot valve (near the bottom of the well) should be installed.

How large is your tank? Is it a bladder tank or bladderless? What are the cut in/out pressures for the pump?

I looked on the tank, I couldn't see a capacity listed on it.
Cut in is about 30, out is about 60.

This is the label off the side of the tank...

Bladder or bladderless?? No idea the air filler is on the top...

This post was edited by gtrshop on Wed, Apr 24, 13 at 20:25

The pump is a Simer, btw

Must be a shallow well, less than 20 feet. I see only one pipe from the pump to the well. Deeper wells require the jet AND the foot valve to be at the bottom of the (two) pipes.
Multi-stage jet pumps are required for wells in the range of 80 to 140 feet deep, depending on the pump selected.

So...after doing a load of laundry the pump cycles....over and over. I think it's because when the pump kicks off the pressure temporarily drops below the low cut in point. When it does that I can somewhat squeeze the hose coming from the pump to the tank, but when the pump kicks on it's nearly impossible to squeeze the hose. It does this over and over even when there is no water running anywhere...

Dont know if that helps

EDIT...

So, I popped the cover off the pressure switch portion of the pump and restricted with a popsicle stick the part that drops down and trips the pump to come on. The water pressure read 25 on the gauge in the water line. A few minute later the water pressure was at 30 or so, and when I removed the popsicle stick the pump stayed off... until I opened the drain valve...I let off only a tiny bit of water and the pump started cycling again.

This post was edited by gtrshop on Thu, Apr 25, 13 at 0:23

Check valves do not last forever.

Mostly the valve seat gets rough and they fail to hold pressure.

You can also get buildup from the water on the sealing faces.

Cycling solved. It's amazing what adding a little air in the tank can do. 28 psi to be precise