Some welcomed what the gallery called a "fresh approach," but others attacked it for omitting several important British and foreign sculptors.
Most outspoken was Andrew Graham-Dixon, writing in the Sunday Telegraph's Seven magazine in his no-star review:
"This lamentable exhibition has no coherence, no clear purpose and fails to mention many of Britain's best sculptors of the past 100 years."
Laura Cumming, of The Observer, drew attention to the absence of pop art, and the lack of "advanced conceptualism."
"And if (Carl) Andre's 'Equivalent VIII' can make the cut, though the American's minimalism never took root here, then why not Marcel Duchamp, whose influence is infinitely greater?"
The exhibition, which runs until April 7, opens with a towering wooden reconstruction of the landmark Cenotaph which stands on Whitehall in London to honor the war dead.
Edwin Lutyens, who designed the original, was actually an architect, and the Royal Academy sought to "demonstrate the formal affinities that exist between sculpture and architecture." It also "manifests the power of the abstract."
In the second room, titled "Theft by Finding," 20th century works stand alongside ancient sculptures from Egypt, India and the Easter Islands, many from other British collections.
"Here you can see how the dialogue between the ancient, the ethnographic and the modern developed," said curators Penelope Curtis and Keith Wilson in the guide.
"Adam," by Jacob Epstein, dominates the third room, and reflects the physical vigor and virility of carving.
Cut from a single piece of alabaster and weighing approximately two tons, its sexually explicit nature meant that it quickly gained notoriety and toured Britain as a kind of freak show before being taken to New York for a peep-show.
The 1938-9 work now stands in the entrance hall to Harewood House, having been bought by the owner.
Another sculpture in the show which caused controversy was Andre's Equivalent VIII, with some members of the press and public objecting to the symmetrical pile of bricks.
It was made in 1966 and purchased by the Tate gallery in London six years later.
The negative reaction appears to have been triggered by a story in the Sunday Times newspaper in 1976, and may explain why American minimalism did not fully take hold in Britain.
By the 1950s, Barbara Hepworth and Henry Moore had become the international face of British sculpture, and the exhibition includes a room dedicated to one work each by the artists.
Moore's bronze "Reclining Figure" is horizontal and figurative, while Hepworth's "Single Form (Memorial)," made of the same material, is vertical and abstract.
U.S. artist Jeff Koons appears with his 1985 work entitled "One Ball 50/50 Tank" in which a basketball floats in a mixture of salt and distilled water inside a glass tank.
In the same room stands Briton Damien Hirst's larger work using a similar method.
"Let's Eat Outdoors Today" (1990-1) comprises two large glass boxes containing a barbecue with meat and plastic table with food as well as thousands of flies, both dead and alive.
The Independent's Charles Darwent described such juxtapositions as "own goals":
"To prove its subject's international credentials, the curators have included works by foreign artists, who largely wipe the floor with their British followers, and in any case got there first," he wrote.
Reporting by Mike Collett-White, editing by Paul Casciato