Thousands of well-wishers and mourners gathered to pay their last respects to the Duke of Devonshire on Monday.
The duke was buried in a village on the Chatsworth estate
The Duke, 84, who died at Chatsworth House on 3 May, was one of the richest men in the UK.
He was buried at St Peter's Church in the estate village of Edensor - a mile from Chatsworth House - on Monday afternoon.
Members of staff from the house and
estate lined the route as the cortege left Chatsworth House for the church.
They were joined by members of the public, many of whom listened to the service on loudspeakers outside.
As the coffin approached the church it passed through an honour guard from the Coldstream Guards.
The Duchess followed the coffin, accompanied by her son Lord Hartington, 60, who will become the 12th Duke of Devonshire on Tuesday.
The Duchess was accompanied by her son Lord Hartington
On the coffin - made of Chatsworth oak - were the Duke's medals, including the Military Cross.
The Duke won the honour during World War II, which claimed the life of his elder brother, thereby handing him the title of Duke of Devonshire.
The 30-minute service included a reading of the Philip Larkin poem At
Grass, and the hymn I Vow to Thee, my Country.
The Duke was laid to rest in the family plot alongside his father, the 10th Duke of Devonshire.
The Duke served in the Coldstream Guards during the war, and was Mayor of
Buxton from 1952 to 1954.
Later, he was a minister in the Conservative government, between 1960 and 1964, led by his uncle, Harold Macmillan.
On 20 September 1998, the Duke and Duchess became the longest-serving holders
of the Devonshire dukedom, having held the title for 17,101 days.
The Duke was a close friend of the Prince of Wales.
The Prince was unable to attend the funeral due to a pre-arranged private
visit, a Clarence House spokesman said.
All Chatsworth attractions and businesses were closed for the day, except for the garden which was open at no charge.