The floor drain at the low point in basement is backing up when we do laundry. The floor drain is only about 5 feet from the tub where the washing machine empties. (We do use a mesh sock over the spout as it empties the washing machine into the sink to help keep junk out of the drain.)
In picture 1, you can see the floor drain. Is this the cap I should remove to try and snake this line?
In picture 2, you can see the laundry tub drain. Is that another cleanout plug that can be removed to snake from there too?
It's possible that the main cleanout that goes out of the house to the city sewer in the street has issues too.Tree roots were an issue for previous owner, and we had that line snaked with a 6" bit just over 2 years ago when we bought house. We have since removed the Norway maple in the yard.
(I'm not seeing a way to attach pictures)

OK here they are
http://i563.photobucket.com/albums/s...floordrain.jpg
http://i563.photobucket.com/albums/s...rytubdrain.jpg

You need to snake that entire Washing machine/floor drain line. I am assuming that they are all on the same line. So start by pulling the clean out plug on the tub drain and use a 1/2 inch snake. Snake it all the way to the mainline and hopefully that would clear it out.

Good luck (former Roto Rooter guy)

You have a partial blockage downstream from the floor drain. Normal discharges will pass but your washer discharges with so much force and volume that it builds up behind the clog and backs up out of your floor drain.
Solution:
Locate and open up the sewer line cleanout. Now cycle the washer and watch the cleanout. If it backs up then ssnake to the street. If the floor drain backs up snake from the clean out in picture#2. Good luck, Tom