Mourning Becomes Electra takes many of its plot elements from the Oresteia by Aeschylus, including the mother of the family taking a lover while the father is at war, killing her husband, and in turn being killed (directly or indirectly) by her children. Despite these plot elements, O'Neill's play is distinctly modern. It is a psychological drama rather than a classical one.

First, although the characters are from a wealthy family, they are not royalty and thus the play is about individual people rather than the broader civic implications of the original trilogy. It is a psychological drama focused on human feelings and motivations and lacks Aeschylus's concern with the gods and fate. Additionally, justice is more personal than universal, despite O'Neill's effort to introduce more general themes. 

In staging, although O'Neill wants the acting style to reference ancient tragedy, the play is still basically modern. Women are played by female actors. Actors do not wear masks. The play is written in prose rather than verse, and Seth, although serving a function similar to the chorus and even singing briefly, is not the equivalent of a full Greek chorus, which sings and dances for long periods between episodes. 

This play is actually made up of 3 different plays, a trilogy:  The Homecoming, The Hunted, and The Haunted.  To begin, then, let's define "tragedy":  "a dramatic composition, often in verse, dealing with a serious or somber theme, typically that of a great person destined through a flaw of character or conflict with some overpowering force, as fate or society, to downfall or destruction" (www.dictionary.com).  In these 3 plays, we have characters that all deal with tragedy, including suicides and murder.  Tragic characters have one distinct flaw, and the characters in these 3 plays are no exception.  For example, Brant's tragic flaw is his obsession with revenge, which leads him to murder, so this play is definitely a modern tragedy.  Also, the play is based on a Greek tragedy.  eNotes states: "In the play, he adapts the Greek tragic myth Oresteia to nineteenth-century New England" (eNotes).