By thermal-based removal of material, for instance by way of laser drilling or laser ablation, the material is removed from the article (2) in form of steam or drops. The material is removed by being subjected to a short-term intense laser pulse (4) causing a generation of considerable pressure from vaporised and/or ionised material. As a result, vaporised melt material is sprayed to the sides or upwards along the sides of a drilled hole. These squirts can either damage the surface around the processed area or result in an upward burr. The method according to the invention provides an additional local steam/plasma pressure causing the ejected material to change direction in such a manner that the surface of the material is not damaged or a stricking burr is not formed. The local steam/plasma pressure can, for instance, be provided by an intense secondary laser beam being emitted downwards and towards an area around the processing location.