Is "Macbeth" a greek tragedy?

As appletrees said, Shakespeare's play cannot be a Greek tragedy because it is an English play.  However, it is like a Greek tragedy in the sense that Macbeth has many of the qualities of a tragedy.  According to a guide on Greek tragedy provided by Grand Valley State University (see link in sources), a Greek tragedy is defined as a play that shows the destruction of a tragic hero through "hubris (pride), fate, and the will of the gods."  One could certainly make a case that Macbeth meets all three criteria by showing how Macbeth is ultimately destroyed because of his desire for power and position (a sense of pride is what causes us to desire these things), because of his chance meeting with the witches (fate), and because of the role the witches (are they gods?) played in leading Macbeth down a path of delusion.

Further, one could easily prove that Macbeth is indeed a tragic hero.  VCCSLitonine provides an excellent summary of Aristotle's ideas about tragic heroes.  A tragic hero must be of noble birth or high stature (Macbeth certainly is), he must be imperfect or fallible (consider how easily manipulated Macbeth is), he must have a tragic flaw (his murderous desire for power and his weak nature that allows him to be manipulated by both his wife and the witches), his downfall must be a result of his own choices (he has ample opportunity to spare Duncan's life, but he chooses power instead), his fate is not wholly deserved (this would be the hardest one to prove, but one might point out that had it not been for the witches and Lady Macbeth, Macbeth himself would have never chosen the path he took), he must ultimately accept his demise with nobility and grace, recognizing his fatal flaw in the end (which Macbeth clearly does in the final scenes of the play.