In 1986, he directed the first production at the RSC's new Swan Theatre: The Two Noble Kinsmen by William Shakespeare and John Fletcher, with Gerard Murphy, Hugh Quarshie and Imogen Stubbs, and served there as Artistic Director until 1991.
He pioneered Marlowe's plays in The Swan with The Jew of Malta (1987) and Dr Faustus (1989) and staged rare works such as James Shirley's Hyde Park (1989) with Fiona Shaw and Alex Jennings.
In 1983 and 1985, Kyle directed The Dillen for the RSC which was an immersive and peripatetic production with a cast of 250 about the epic life of a local man, George Hewins, which was staged on the streets and in the fields of Stratford.
He later adapted and directed Shakespeare's Henry VI for Theatre For A New Audience in New York, which won a Drama Desk award for Most Outstanding Revival.
Kyle has been nominated in the Laurence Olivier Awards as Best Director for his RSC productions of The Taming of the Shrew and Love's Labour's Lost.