The institute, backed by actor Robert Redford, holds its film festival every January, but the theatre programme had begun two years before its film programme.
For nearly 27 years, it has invited playwrights, directors and performers to workshops in the United States, where they learn to hone their craft.
From 14 to 16 April, the programme will stage 2004's Pulitzer Prize winning drama, I Am My Own Wife, at the Stary Theatre in Krakow, Poland, and hold workshops with playwright Doug Wright and director Moises Kaufman.
"We have the belief that artistes need to be communicating with artistes from different countries," said Philip Himberg, Producing Artistic Director of the Sundance Theatre Programme.
I Am My Own Wife was developed within the Sundance programme by Wright, an American, and tells of an East German transvestite who survives under the Nazis and the Poland's communist government.
Himberg said many emerging playwrights in Poland are now writing introspective, personal stories rather than the political and social dramas favoured during and after the collapse of the Soviet Union.
"It's really interesting to see how they are coming to grips with this part of their life, and we want to be there to help develop it and support it," Himberg said.
Sundance is developing more programmes with international components. This year it held competitions for foreign language films at its festival to give them more media exposure.
The institute also established a pool of funds in 2002 to help international filmmakers create documentaries. The fund was designed to support up to 50 projects a year.