Cave Underhill (1634–1710?) was an English actor in comedy roles.
Underhill entertained three generations of London theatre-goers. For over 40 years, as a member of the Duke's Company, Underhill played the first Gravedigger in Hamlet. He was also successful in playing Gregory in Romeo and Juliet, the clown in Twelfth Night, and Trinculo in The Tempest.
The son of Nicholas Underhill, a clothworker, he was born in St. Andrew's parish, Holborn, London, on 17 March 1634, and was admitted to Merchant Taylors' School in January 1645. He became first a member of the acting company which was gathered by John Rhodes. around Thomas Betterton. He was then recruited for Sir William D'Avenant and the Duke of York's company at the theatre in Lincoln's Inn Fields. In 1663 he was fined in an assault case, with Betterton and James Noke.
The first character to which Underhill's name appears is Sir Morglay Thwack in D'Avenant's comedy The Wits, revived, with alterations, at Lincoln's Inn Fields on 15 August 1661. In Abraham Cowley's Cutter of Coleman Street, he was the same season the original Cutter, a swaggerer. In 1662 he played before the king and queen at Whitehall Palace the title part in an English version of Ignoramus. After the theatre had been closed for eighteen months through the Great Plague and Great Fire of London, he was the first Moody in John Dryden's Sir Martin Marrall on 16 August 1667, second performance.
On the opening in 1671 of the new theatre in Dorset Gardens, Underhill was the original Sir Simon Softhead in Edward Ravenscroft's Citizen turned Gentleman (based on Monsieur de Pourceaugnac). He played also Pedagog in Lord Orrery's Mr. Anthony.