My washing machine water is coming out of drainage pipe in backyard, which is suppose to be buried underground. I can stand out doors and watch it come out of big black pipe. Would a plumber be able to correct this problem?

Would a plumber be able to correct this problem?
If you're handy you can do it yourself. A dry well ,(see image) is about the best way. Good luck, Tom

Like Tom says you can do it yourself or call a handyman in to dig for you. Are you on city sewer or septic? Not sure where you are located but most codes require even gray water to not be dumped into open air.

In addition to the above advices: It could also be that the "black pipe" is an uncapped Clean Out. If that's the case than you can use it to insert snake and to clean your sewer drain. In any case, if it is really a Clean Out than make sure you cap it.