Last Portrait of Mother by Daphne Todd is among three portraits in the running for the £25,00 prize.
It was painted shortly after Annie Mary Todd's 100th birthday, and is described as a devotional study by the artist.
David Eichenberg and Michael Gaskell are also shortlisted for the award, which is now in its 31st year at the National Portrait Gallery in London.
'Outstanding year'
Eichenberg's work, titled Tim II, shows his friend - sculptor Timothy A Stover, seated at a metal bandsaw in the fabrication shop in which he works, located directly below the artist's studio in an old warehouse in Toledo, Ohio.
The artist said he wanted the painting to 'read like a work by Holbein' where every item in the portrait represents an aspect of the sitter.
Gaskell, who was runner-up last year, spotted his subject, Harry, while out shopping.
His wife persuaded Gaskell to approach him, and the painting was completed earlier this year.
This year's award attracted a record 2,177 entries - up 276 on last year - and 58 portraits have been selected for the exhibition at the gallery.
Sandy Nairne, director of the National Portrait Gallery, said: 'The 2010 BP is another outstanding year for the quality of the entries and the range of styles. I am grateful to all the many artists who submitted, and to BP for their continuing support.'
The winner will be announced on the 22 June. The exhibition will run from 24 June until 19 September.
In addition to a prize of £25,000, the winner of the award will receive a commission worth £4,000.
Text and image by bbc.co.uk
