Dame Helen is nominated for her roles in The Woman in Gold and Trumbo, while Elba is nominated for Beasts of No Nation and BBC drama Luther.
Eddie Redmayne, last year’s SAG best actor winner, has been nominated again for his performance as transgender pioneer Lili Elbe in The Danish Girl.
The awards are often seen as key indicators for the Oscars.
For the past 10 years, the winner of the best actor category has gone on to triumph at the Academy Awards.
If Redmayne was to triumph, he would be the first actor to win twice in a row since Tom Hanks in 1994 and 1995.
Dame Helen is nominated for best actress in The Woman in Gold in which she plays real-life Jewish World War Two survivor Maria Altmann, who fought the Austrian government over Gustav Klimt paintings stolen from her family.
She will compete against Saoirse Ronan for Brooklyn, Sarah Silverman for I Smile Back, Brie Larson for Room and Cate Blanchett for Carol.
Dame Helen is also nominated for best supporting actress and as an ensemble cast member for Trumbo, about the real life Hollywood screenwriter Dalton Trumbo.
In the best supporting actress category, she is recognised alongside Rooney Mara for Carol, Rachel McAdams for Spotlight, Alicia Vikander for The Danish Girl and fellow Brit Kate Winslet in Steve Jobs.
As well as his ensemble cast nomination for Beasts of No Nation, Elba receives a best supporting actor nod for his part as the charismatic but ruthless Commandant in the film, who keeps his young recruits in his thrall in the African warfare picture.
He is nominated alongside two more Brits – Mark Rylance in Bridge of Spies and Christian Bale for The Big Short, alongside Michael Shannon in 99 Homes and nine-year-old Jacob Tremblay for Room.
Elba’s other nomination is for his starring role in Luther, recognised in the TV movie/miniseries category.
Redmayne has been nominated for a second consecutive year in the best actor category.
The star is nominated alongside Michael Fassbender for Steve Jobs, Leonardo DiCaprio for The Revenant, Bryan Cranston for Trumbo, and Johnny Depp for Black Mass.
Trumbo, The Big Short, Spotlight, Straight Outta Compton and Beasts of No Nation are all nominated for their ensemble cast performances.