The British stars have earned Best Actress and Best Actor nominations, respectively, at the annual awards ceremony which recognises outstanding theatre productions and performances, ranging from plays, musicals and dance.
Judi - who was recently nominated for an Oscar for 'Philomena' - leads the Best Actress race for 'Peter and Alice', competing against Hayley Atwell ('The Pride'), Anna Chancellor ('Private Lives') and Lesley Manville ('Ghost').
Meanwhile, Jude is up for Best Actor for his regal performance in 'Henry V', however, he faces stiff competition from fellow screen star Tom Hiddleston for 'Coriolanus', as well as Rory Kinnear ('Othello') and Henry Goodman ('The Resistible Rise Of Arturo Ui').
Film director Sam Mendes' new stage adaptation of 'Charlie and the Chocolate Factory' leads the way for most nominations this year, tying Stephen Sondheim's 'Merrily We Roll Along' with seven nods apiece.
Mark Rubinstein, president of governing body the Society of London Theatre, said: ''Congratulations to all of this year's Olivier Award nominees whose incredible talents lit up the West End and contributed to another record-breaking year.''
The Olivier Awards take place on 13 April at London's Royal Opera House.
2014 Olivier Awards, selected nominations:
BBC Radio 2 Audience Award:
'Les Misérables' at the Queen's Theatre
'Matilda the Musical' at the Cambridge Theatre
'The Phantom of the Opera' at Her Majesty's Theatre
'Wicked' at the Apollo Victoria Theatre
MasterCard Best New Musical:
'The Book of Mormon' at the Prince of Wales Theatre
'Charlie and the Chocolate Factory' at the Theatre Royal Drury Lane
'Once' at the Phoenix Theatre
'The Scottsboro Boys' at the Young Vic
'The Amen Corner' at the National Theatre, Olivier
'Ghosts' at the Almeida Theatre & Trafalgar Studios
'Othello' at the National Theatre, Olivier
'Private Lives' at the Gielgud Theatre
Best Musical Revival:
'Merrily We Roll Along' at the Harold Pinter Theatre
'The Sound of Music' at the Regent's Park Open Air Theatre
'Tell Me on a Sunday' at the St James Theatre & the Duchess Theatre
Best New Play
'1984' at the Almeida Theatre
'Chimerica' at the Almeida Theatre & Harold Pinter Theatre
'The Night Alive' at the Donmar Warehouse
'Peter and Alice' at the Noël Coward Theatre
Best New Comedy:
'The Duck House' at the Vaudeville Theatre
'The Full Monty' at the Noël Coward Theatre
'Jeeves & Wooster in Perfect Nonsense' at the Duke of York's Theatre
'The Same Deep Water As Me' at the Donmar Warehouse
Henry Goodman for 'The Resistible Rise Of Arturo Ui' at the Duchess Theatre
Tom Hiddleston for 'Coriolanus' at the Donmar Warehouse
Rory Kinnear for 'Othello' at the National Theatre, Olivier
Jude Law for 'Henry V' at the Noël Coward Theatre
Hayley Atwell for 'The Pride' at the Trafalgar Studios
Anna Chancellor for 'Private Lives' at the Gielgud Theatre
Judi Dench for 'Peter and Alice' at the Noël Coward Theatre
Lesley Manville for 'Ghosts' at the Almeida Theatre & Trafalgar Studios
Best Actor in a Supporting Role:
Ron Cook for 'Henry V' at the Noël Coward Theatre
Mark Gatiss for 'Coriolanus' at the Donmar Warehouse
Jack Lowden for 'Ghosts' at the Almeida Theatre & Trafalgar Studios
Ardal O'Hanlon for 'The Weir' at the Donmar Warehouse & the Wyndham's Theatre
Best Actress in a Supporting Role:
Sharon D Clarke for 'The Amen Corner' at the National Theatre, Olivier
Sarah Greene for 'The Cripple Of Inishmaan' at the Noël Coward Theatre
Katherine Kingsley for 'A Midsummer Night's Dream' at the Noël Coward Theatre
Cecilia Noble for 'The Amen Corner' at the National Theatre, Olivier
Best Actor in a Musical:
Gavin Creel for 'The Book of Mormon' at the Prince of Wales Theatre
Jared Gertner for 'The Book of Mormon' at the Prince of Wales Theatre
Douglas Hodge for 'Charlie and the Chocolate Factory' at the Theatre Royal Drury Lane
Kyle Scatliffe for 'The Scottsboro Boys' at the Young Vic
Best Actress in a Musical:
Rosalie Craig for 'The Light Princess' at the National Theatre, Lyttelton
Zrinka Cvitešić for 'Once' at the Phoenix Theatre
Jenna Russell for 'Merrily We Roll Along' at the Harold Pinter Theatre
Charlotte Wakefield for 'The Sound of Music' at the Regent's Park Open Air Theatre
Best Performance in a Supporting Role in a Musical:
Stephen Ashfield for 'The Book of Mormon' at the Prince of Wales Theatre
Colman Domingo for 'The Scottsboro Boys' at the Young Vic
Josefina Gabrielle for 'Merrily We Roll Along' at the Harold Pinter Theatre
Nigel Planer for 'Charlie and the Chocolate Factory' at the Theatre Royal Drury Lane
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