Knightley was nominated for a best supporting actress award for The Misanthrope, her West End debut.
In the best actor category, Law is shortlisted for his portrayal of the title role of Shakespeare's Hamlet, while James McAvoy, also best known for his films, is nominated for Three Days of Rain.
With six nominations apiece are Lucy Prebble's Enron, about the collapsed U.S. energy trading company, and Jerusalem, Jez Butterworth's portrayal of less-than-idyllic life in rural England.
The Royal Court Theater garnered the most nominations with 15, followed by the Donmar with 10 and the National Theater with nine.
London's West End enjoyed a bumper 2009, with attendances rising 5.5 percent to 14.3 million and revenues 7.6 percent higher than 2008 at 505 million pounds ($790 million).
Following is a list of the main categories for the 2010 Laurence Olivier Awards, to be handed out in London on March 21.
Best Actress
- Gillian Anderson/A Doll's House
- Lorraine Burroughs/The Mountaintop
- Imelda Staunton/Entertaining Mr Sloane
- Juliet Stevenson/Duet For One
- Rachel Weisz/A Streetcar Named Desire
Best Actor
- James Earl Jones/Cat on a Hot Tin Roof
- Jude Law/Hamlet
- James McAvoy/Three Days of Rain
- Mark Rylance/Jerusalem
- Ken Stott/A View From the Bridge
- Samuel West/Enron
Best Supporting Actress
- Hayley Atwell/A View From the Bridge
- Michelle Dockery/Burned By the Sun
- Alexandra Gilbreath/Twelfth Night
- Keira Knightley/The Misanthrope
- Rachael Stirling/The Priory
- Ruth Wilson/A Streetcar Named Desire
Best Supporting Actor
- Mackenzie Crook/Jerusalem
- Rory Kinnear/Burned By the Sun
- Tim Pigott-Smith/Enron
- Eddie Redmayne/Red
Best Director
- Rupert Goold/Enron
- Michael Grandage/Hamlet
- Lindsay Posner/A View From the Bridge
- Ian Rickson/Jerusalem
- Bijan Sheibani/Our Class
Best New Play
- Enron by Lucy Prebble
- Jerusalem by Jez Butterworth
- The Mountaintop by Katori Hall
- Red by John Logan
