When my washing machine drains, the water backs ups and overflows out of the pipe. I tried to flush out any blockage with a steady flow of water down the pipe and there was no back up or overflow. It only happens when my washing machine drains. What could be the problem?

I am assuming this isn't a new machine. New machines may have a higher capacity pump and it can overwhelm the drain. The steady flow of water will not have enough force to open any blockage, you need to rod that pipe a good 20 feet. Then flush with plenty of hot water.