They came in their millions for the Pope Francis' Copacabana beach party

It is usually synonymous with unbridled hedonism, but Rio de Janeiro's Copacabana beach was transformed into a vast encampment of the faithful on Sunday when three million young Roman Catholics squeezed on to every last inch of sand for the climax of the Pope's week-long visit to Brazil.

Hundreds of thousands had camped overnight on the long, crescent-shaped arc - making it one of the world's biggest slumber parties - before waking up bleary-eyed in time for an open-air Mass conducted by Pope Francis from a vast white stage at the beach's northern tip.

Thousands more descended from the city's suburbs, pushing out the beach volleyball players and bikini-clad women who normally occupy the most famous stretch of "Sin City" at weekends.

The faithful even shunned the popular beach kiosks offering caipirinha and cuba libre cocktails, choosing instead to drink milk and orange juice as they waited for the Pontiff to appear.

The 2.5-mile beach was so crammed that many spilled over on to the promenade and streets behind it, bedding down in front of smart hotels and apartment blocks on strips of cardboard. Giant television screens, of the kind usually seen at a rock concert, stretched the length of the beach to allow everyone a view.

"We had to sleep on the sidewalk because there was no room on the beach. We woke at 6.30am so people are pretty tired," said Steven Santander, 25, an architect from New Jersey and part of a group of 80 young pilgrims.

Julia Kloster, 25, an accountant from Argentina, managed to find room on the sand. "It was great. We weren't cold - we had sleeping bags. We slept well because we were so tired - we are staying two and a half hours out of Rio so we've spent the whole week on buses. But we're very proud that the Pope is Argentinean."

During the Mass, the 76-year-old Pope appealed to the young pilgrims to take what they had learned in Rio and reinvigorate the Church around the world.

Returning to one of the principal themes of his four-month-old papacy, he told them to shake up the stuffy Catholic hierarchy and take the message of Christ "to the fringes of society, even to those who seem farthest away, most indifferent".

He gave them the task of providing the Church with "fresh power", at a time when Catholics in Brazil are deserting in droves, either embracing secularism or joining the growing number of Protestant evangelical churches. He told priests around the world to "be creative, be audacious" in taking the teaching of the Gospel on to the streets in order to "break down evil and violence … intolerance and hatred".

His vast audience, wearing T-shirts that read "I love Papa Francesco" and wrapped in the distinctive green and gold Brazilian flag, applauded and chanted "Long Live the Pope" in several languages.

The Mass was also attended by several South American heads of state, including the presidents of Brazil, Bolivia, Uruguay and the Pope's homeland, Argentina. "Francis can relate to anyone.

He's the people's Pope," said Vincent Haber, 35, a youth minister from Perth in Western Australia. Nicola Speranza, 25, from the Molise region of Italy, said: "He uses language that is very easy to understand.

He speaks in concrete terms - he talks about our lives, our needs. You don't often get that from the Church." On Saturday, in what was interpreted as veiled criticism of his earnest, theologian predecessor, Benedict XVI, the Pope said the Church often used language that many ordinary people found baffling and overly intellectual.

The Church was "perhaps too cold, too caught up with itself, perhaps a prisoner of its own rigid formulas", he said. "At times we lose people because they don't understand what we are saying, because we have forgotten the language of simplicity and import an intellectualism foreign to our people."

He expressed solidarity with the one million Brazilians who last month took to the streets to protest against corruption and rising living costs, in sometimes violent demonstrations.

"I have been closely following the news reports of the many young people who throughout the world and also here in Brazil have taken to the streets in order to express their desire for a more just and fraternal society. I encourage them to continue overcoming apathy and offering a Christian response to the social and political concerns arising in many parts of the world."

In his prepared text, he had added that they should do so in an "an orderly, peaceful and responsible way" but when it came to reading out the address, he omitted that phrase.

After a week-long visit that Vatican aides have called "triumphant", Francis boarded a plane back to Rome. It was announced that the next biennial World Youth Day will be in Krakow in Poland - the homeland of the late Pope John Paul II - in 2016.