Saudi Arabia's King Fahd has been laid to rest in a simple grave at a cemetery in Riyadh.
King Fahd's body, which was wrapped in a brown shroud, was carried by pallbearers into the graveyard in the country's capital. His body was lowered into the ground in an unmarked grave, in line with the kingdom's strict Wahhabi Islamic traditions.
Muslim leaders from around the world gathered in Riyadh to pay their last respects to King Fahd.
Western leaders and dignitaries are due to arrive later to offer condolences after the funeral service, which was held in a Riyadh mosque this afternoon.
President McAleese extended her condolences on behalf of the Irish people.
King Fahd died yesterday after 23 years ruling the strategic Gulf state, which is both the world's biggest oil exporter and the cradle of Islam - drawing more than a billion faithful to turn five times a day toward Mecca in prayer.
Saudi Arabia's new leader, King Abdullah
He is succeeded by his half-brother Abdullah who has run day-to-day affairs since Fahd suffered a stroke in 1995.
Abdullah is expected to maintain Saudi Arabia's commitment to stable oil markets and its close alliance with the West.
Saudis will pledge allegiance to Abdullah, who is at least 80, and the new Crown Prince Sultan tomorrow.
Unlike many Muslim states, Saudi Arabia has set no mourning period, in keeping with Wahhabi acceptance of God's will without question. Saudi flags, emblazoned with the proclamation of faith "There is no God but Allah", flew at full mast.
Ordinary Saudis mixed at the funeral with leaders from across the Muslim world, including Pakistan's President Pervez Musharraf and Syria's President Bashar al-Assad. First to arrive had been Senegal's President Abdoulaye Wade and Afghanistan's President Hamid Karzai.
US President George W. Bush, who has promised a "close partnership" with Saudi Arabia under Abdullah, is sending a delegation. Diplomats say it may include his father, President George Bush, who sent half a million US troops to Saudi Arabia in 1990 to launch the recapture of Kuwait from Saddam Hussein.
Fahd, aged about 83, had been in hospital since May 27th, when he was admitted with acute pneumonia. He ascended the throne in 1982, at the height of the Saudi petrodollar boom, with a reputation as an administrator and international diplomat.
Abdullah, the fifth son of Saudi Arabia's founder King Abdul-Aziz to ascend the throne, is a cautious reformer who has overseen modest economic and political liberalisation.
Analysts say Abdullah's toughest challenges will be to implement political reforms and keep up the fight against Osama bin Laden's al-Qaeda network, which has a waged violent campaign aimed at toppling the Saudi royal family.
Bin Laden has vowed to depose the Saudi royals, whom he has condemned as US "agents and stooges".