The method is used to drill at least one hole into a front wall section of a workpiece (12) by way of a machining jet formed from liquid, to which abrasive material is admixed as needed. As seen looking in the drilling direction, the front wall section is located in front of a rear wall section of the workpiece, which is disposed with an intermediate space at a distance from the front wall section. The hole is drilled at least partially by the machining jet impinging on the front wall section in a pulsed manner. This pulsed jet is generated by the recurrent interruption of the impingement of the liquid and/or of the abrasive material on the front wall section.