This play has several tragic elements. The relationship between the two central characters - Marcus Brutus and Julius Caesar - becomes deeply tragic, as the two are actually good friends, yet Brutus feels compelled by his political principles to kill his friend. Brutus agonises over this before finally being persuaded by Cassisus. Caesar, when attacked by the conspirators is finally undone when he sees his friend also aiming a blow at him. Thus, in terms of character, the play is tragic at its heart.
The play is also tragic in a wider sense. Brutus and the other conspirators kill Caesar for the greater public good, to prevent Caesar from becoming a tyrant who will oppress the people. Yet, as we see at Caesar's funeral, the public are completely incapable of appreciating or even understanding this, and are persuaded by Antony to turn against the conspirators. Instead of leading to peace and a better society, as Brutus hoped, the murder of Caesar leads to more war and power struggles which ultimately result in the establishment of Rome's first emperor, Augustus, which is exactly the kind of thing that Brutus wanted to prevent. The tragedy is that all his ideals essentially come to nothing.