The test is designed to replicate what happens when one-fourth of a car's front end strikes another car or a fixed object like a tree or utility pole at 40 mph.
Of the 11 cars tested from the 2012 model year, only the Acura TL, Volvo S60 and Infiniti G earned good or acceptable ratings from the institute.
Four cars earned marginal ratings. They're the Acura TSX, BMW 3 Series, Lincoln MKZ and Volkswagen CC.
And four other cars earned poor ratings: the Mercedes C-Class, Lexus IS 250, Audi A4 and Lexus ES 350.
The institute says the new test indicates that side air bags may not go off in time or extend far enough in off-center, frontal crashes.
Non-luxury models will be tested next.