My kenmore washer continues to fill up with water. Once the washer has reached capacity the runs out everywhere from the bottom of washer. To drain water out I can place it on spin and it spins all wter out correctly. What seems to be the problem, and how can it be fixed??

There's an electronically controlled valve (perhaps a solenoid), which lets the water into the washer at the correct time... and for the correct length of time. I suggest this valve or solenoid is faulty. Cheers!

How do you get the water to stop? If you have to turn the taps off on the wall then it is a water valve problem. If you can push in the timer (to the off position) then you either have a plugged air bell or a hole in your pressure tube from the air bell to the pressure switch or your pressure switch is the problem.