Mathematical model for hyperboloid grinding of twist drill and relationships between drill design and grinding parameters are introduced.Point angles at outer corner and chisel edge corner are proposed to be used as the drill design parameters to determine the type uniquely and the relicf andgle is used as a supplement parameter.Function relations between the twist drill design and the grinding parameters are derived.Hence a theeoretical basis is estab-lised for design and grinding of the hyperboloid twist drill.