Biden, eldest son of US Vice-President Joe Biden, died of brain cancer Saturday at age 46.
Beau Biden lay in honor in the Senate chamber following a processional from Wilmington to Dover. His flag-draped casket sat in front of a Senate dais draped with black bunting and decorated with white flowers. The casket was flanked by a black-and-white photo of Biden with his wife and children and a Conspicuous Service Cross presented to him posthumously Thursday for his service in the Delaware National Guard.
Gov. Jack Markell led the tributes for Biden in a 25-minute service attended by state officials, lawmakers and other dignitaries. Beau Biden's son Hunter, and daughter Natalie, clung to their mother, Hallie, and grandmother, Jill Biden, during the service.
The Biden family, led by Joe Biden, then stood in a receiving line, warmly greeting well-wishers with hugs and handshakes, punctuated by both smiles and tears, as recorded harp music played softly in the background.
The doors were then opened for other members of the public.
Col. Ed Brandt, a Delaware National Guard chaplain, said Biden's life was marked by many accomplishments between "bookends of tragedy."
Biden was 3 years old when he and his younger brother, Hunter, were injured in a 1972 car crash that killed their mother and infant sister. The crash occurred just weeks after Joe Biden was elected to the US Senate. He was sworn into office at his sons' hospital bedside.
Beau Biden's life and political career were cut short by cancer, which first appeared in the form of a lesion discovered by doctors in 2013, three years after he had suffered a minor stroke.
Thursday's services are the first in a series of public commemorations, which include a viewing at St. Anthony of Padua church in Wilmington on Friday, followed by a Saturday funeral Mass at which US President Barack Obama will deliver a eulogy.