I have a 10` peace of pipe under my basement floor that is not vented. It is clean. I snaked it. But my washer water still backs up Is not having a vent the problem??

10' long but what diameter" Can you take a picture?

It looks to be about 2 1/2" or 3". It is all under a concrete floor.

A 2" or larger is what you need, if it still backs up you aren't rodding it fully. What are you rodding with?

Please start with the washer and tell us how it's piped. Telling us that your drainage's under the slab doesn't help. Is there a stand pipe that's trapped? Could you install a AAV, (see image) just downstream from the trap? Let's have more details. Regards, Tom