The RSC has kicked off its hugely ambitious programme of staging the Complete Works of Shakespeare at Stratford-upon-Avon, promising that the festival will be, in the words of the artistic director, Michael Boyd, “the greatest show on earth”. Is such braggadocio justified? On the evidence of these first two shows, a satisfying Romeo and Juliet and an absolutely storming Antony and Cleopatra, it just might be.

Both plays are about the tragic deaths of lovers in a world rent by violence and war. The two star-cross’d lovers from Verona are the innocent young victims of parental vindictiveness and a petty, squabbling society. Juliet, especially — “my lamb”, born on Lammas/Lamb-mass Eve — is the sinless white sacrifice whose ritual death will shame the feuding families into peace. Never, indeed, was there a story of more woe than this of Juliet and her Romeo. Their fate has always been uniquely heartbreaking. They should have lived. Whereas for the older, slightly wiser and much vainer Antony and Cleopatra, their tragedy is just another aspect of their own glamour. Cleopatra in particular, that ultimate drama queen, stages and relishes her death just as she did her life and love. They are both posturing celebrities, laughable, ludicrous — and lovably human with it.

Harriet Walter inhabits her role as the “serpent of old Nile” to perfection: the bewitching middle-aged woman still given to adolescent temper tantrums that, bafflingly, only add to her allure. Patrick Stewart is a less obvious, oldish Antony, with fuzzy white hair, and his years bring an added pathetic quality to the soldier’s fall. He has to work hard to stand out, however, for there are so many other superlative performances and potent stage presences here. In fact, where Gregory Doran’s production really scores is in its furious, pumped-up macho energy.

You have never seen such high- testosterone Shakespeare, espe- cially from Ariyon Bakare as Pompey, Joseph Alessi as Philo and David Rubin as a swaggering, piratical Menas, like an extra from Gladiator, but with rather better diction. The machismo is only emphasised by superb costume design from Kandis Cook, all embossed leather breastplates, buckled vambraces and footwear suggesting jackboots. All combine in the awesome and slightly terrifying drinking scene, with the men clanking goblets over swinging trestle tables, joining together in a stomping percussive dance and roaring with laughter at poor, tiddly Lepidus, the Iain Duncan Smith of the triumvirate. (James Hayes even looks like IDS.) There are no skippy, girlie thespians here. The entire crew look as if they have spent the past six months in the gym, and the effort pays off. The play is not only one of the great love stories, but also profoundly about ideas of virtue, Roman virtus — literally, manliness.

Also exceptional are John Hopkins as Octavius (later Emperor Augustus), a joyless puritan so uptight that he teeters on the brink of madness; Ken Bones as Enobarbus, as good as you will ever see; and special mention for Craig Gazey as the Messenger, for squeezing the maximum pleasure out of a small part (no Shakespearian bawdry intended).

Away from the smaller, more intense indoor Globe that is the Swan, there’s Nancy Meckler’s new version of Romeo and Juliet in the main house. It boasts a powerful and boldly interpolated opening scene in which the perennially bickering Montagues and Capulets give up their weapons in a general arms amnesty, and a new hope seems to dawn with it. False dawn. They are soon fighting again. Yet the substitution of a kind of ritualised, non-contact stick play for the traditional swordfights seems badly misjudged, with Tybalt, Mercutio and Romeo skipping round each other like morris men armed with snooker cues. The bleak-looking set proves versatile, though, with a metal gantry serving for the balcony scene, and Romeo swinging on it like an excited Whipsnade gibbon.

The two leads, Morven Christie as Juliet and Rupert Evans as Romeo, are engaging, Sorcha Cusack is an enjoyably infuriating Irish nurse and David Fielder an outstanding Friar Laurence: an early exponent of muscular Christianity, sporting something like a Yorkshire accent, bluff, tough and no-nonsense, yet finally as broken by the deaths of the two young lovers as anyone.

The Complete Works Festival is working well so far. On, on, lusty gentlemen.

Antony and Cleopatra, four stars
Swan Theatre, Stratford-upon-Avon

Romeo and Juliet, three stars
RST, Stratford-upon-Avon