The show "Donny & Marie" incorporates singing, dancing, comedy, audience interaction and their signature brother-sister banter, the resort said.
The 90-minute production marks the first time in 29 years that the siblings have performed an extended residency engagement in Las Vegas.
"The audience response to 'Donny & Marie' has been overwhelmingly positive," Don Marrandino, president of Flamingo Las Vegas, said in a statement. "Each night they perform to a packed showroom and receive standing ovation after standing ovation. Donny and Marie fans are coming from all over the country and all parts of the globe to see this show; they give people another reason to come to Las Vegas."