Castelli, who was diagnosed with cancer last fall, died of pneumonia.
The New Jersey-born dancer trained at NYCB's School of American Ballet, and joined the company in 1971.
The soloist role in Balanchine's Gigue was created by the choreographer for Castelli, although an injury prevented him from premiering the role (it was performed by Christopher d'Amboise instead). Later, it became one of Castelli's signature performances. Castelli also created roles in other Balanchine ballets, including PAMTGG, Gaspard de la nuit, and Union Jack.
In repertory works he was known for such Balanchine roles as the title role in Prodigal Son, the poet in La sonnambula and the quivering sigh in Variations pour une porte et un soupir. He also danced in Robbins' Dances at a Gathering and Watermill.
Castelli retired from performing in 1990, and stayed on with the company as a ballet master, rehearsing Balanchine and Robbins works for the company and staging works for other companies around the country. He also served on the Robbins Rights Trust advisory committee, helping preserve the choreographer's repertory.