An experimental investigation has been carried out into the drilling of carbon and glass fibre-reinforced polymer composite materials. Both materials have been manufactured from prepreg by the hand lay-up method and cured in an autoclave as per the manufacturer's recommended curing cycles. Experimental tests have been conducted by means of a comparison between two drills of different geometry and structure: a standard high-speed steel (HSS) twist drill and a multifacet carbide drill. Both drills have been used with a series of controlled cutting parameters. Optical microscopy has been used to inspect drilled parts and decisions relating to the optimum machining conditions were based on an envelope of damage, factor of delamination (Fd) and appearance of the produced holes. On the basis of this analysis, methods are suggested to improve machining conditions by applying variable cutting parameters and damping effects.