Vice-President Joe Biden led a procession into the church with his family at the beginning of the service.
Mourners heard President Obama describe Mr Biden as a public servant who learned through early tragedy what mattered most and as a result decided upon living “a life of meaning” that would inspire those around him.
“He was a scion of an incredible family,” the president said, “who brushed away the possibility of privilege for the harder, better reward of earning his own way.”
The president described Beau Biden as a son, a father, a soldier and a politician who refused to take short cuts in his determination to serve his country and others.
He said that a “cruel twist of fate” killed Beau Biden’s mother and infant sister in a car crash four decades ago and left Beau – three years old at the time – and his younger brother Hunter in hospital.
The accident happened shortly after Mr Biden won election to the Senate in 1972.
Mr Biden was diagnosed with brain cancer in August 2013 and underwent treatment that was initially successful. However, the cancer recurred earlier this year.
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