Introduced in 1959, the third series of the Sunbeam Rapier was available with hard top or cabriolet bodywork. The engine was initially the 1494cc 4-cylinder already used on the second series. From April 1961 the Rapier was updated with a new 1592cc 4-cylinder engine, which would also be kept on the next series. With the 80 horsepower of the 1592cc version, the Rapier was capable of quite brilliant performance. The Rapier MkIII went out of production in 1963. About 15,000 examples were built with the 1.5-liter engine and about 17,000 with the 1.6-liter engine.