Method of generating a machining program that can be interpreted by a physical controller of a numerical control machine tool, this machine tool comprising several moving parts able to move relative to one another so as to move an actual tool with respect to an actual workpiece that is the starting point for a component that is to be machined, the actual tool being borne by one of the moving parts and the actual workpiece by another of the moving parts via means for holding the actual workpiece in position, the method of generating a machining program being essentially characterized in that the machining program is generated from: - a prerecorded set of machine parameters representative of the machine tool, some of these machine parameters being representative of space volumes each one representative of at least one of the said moving parts of the machine tool and other machine parameters being representative of kinematic links between at least some of the said moving parts of the machine; and - a prerecorded set of machining sequences, each machining sequence being representative of an expected movement of the actual tool during part of the machining of a component; on the basis of at least some of the said machine parameters and of at least some of the machining sequences, a computer simulation program carries out machining feasibility tests, the machining program being generated in a format that can be executed by the said physical controller only if it passes the machining feasibility tests beforehand, and one of the machining feasibility tests is a test on the kinematic feasibility of the machining that involves checking, as a function of the prerecorded set of machine parameters and as a function of the prerecorded set of machining sequences, that the machine tool is capable of moving the actual tool in accordance with each of the machining sequences and in accordance with link paths, each link path being representative of an expected movement of the actual tool between two of the said machining sequences that immediately succeed one another. - a prerecorded set of machine parameters representative of the machine tool, some of these machine parameters being representative of space volumes each one representative of at least one of the said moving parts of the machine tool and other machine parameters being representative of kinematic links between at least some of the said moving parts of the machine; and - a prerecorded set of machining sequences, each machining sequence being representative of an expected movement of the actual tool during part of the machining of a component; on the basis of at least some of the said machine parameters and of at least some of the machining sequences, a computer simulation program carries out machining feasibility tests, the machining program being generated in a format that can be executed by the said physical controller only if it passes the machining feasibility tests beforehand, and one of the machining feasibility tests is a test on the kinematic feasibility of the machining that involves checking, as a function of the prerecorded set of machine parameters and as a function of the prerecorded set of machining sequences, that the machine tool is capable of moving the actual tool in accordance with each of the machining sequences and in accordance with link paths, each link path being representative of an expected movement of the actual tool between two of the said machining sequences that immediately succeed one another.