Shue was born in New Orleans and grew up in Chicago, Illinois. He graduated from Illinois Wesleyan University in 1968, served in the Army, and then began his career as a professional actor and playwright. He worked in repertory and in New York, and appeared in the television series One Life to Live. Film appearances include A Common Confusion and The Hungry Leaves.
The Nerd premiered in April 1981 in Milwaukee, and was produced successfully in London's West End. It transferred to Broadway in 1987. It is a simple character-based comedy, in which a normal dinner party, interrupted by the house-guest from hell, dissolves into hilarious insanity.
The Foreigner premiered in 1983, and transferred to 'off-Broadway'. A similarly farcical comedy, the central character is Charlie, who, while on a vacation in a Georgia hunting lodge, pretends not to be able to understand English, so as to avoid the attentions of the other guests. His plan backfires and he soon finds himself the confidant of everyone there, and having to foil the schemes of the local KKK chapter without revealing his secret.
The Foreigner was still running at the time of Shue's death. He was killed in the crash of a commuter plane in the Shenandoah Valley in Virginia. Both The Nerd and The Foreigner have become staples of the professional and amateur theatre. His other plays include: