The invention relates to a procedure for etching of materials at the surface by focussed electron beam induced chemical reaction at the surface, with the following steps: a) in a vacuum atmosphere the material which is to be etched is irradiated with at least one beam of molecules and at least one first beam of electrons, whereby the irradiated material and the molecules of the beam of molecules are excited in a way that a chemical reaction takes place and forms a reaction product, which is not gaseous/not volatile—reaction step. The invention is characterized in that b) the reaction product is evaporated from said surface by an second beam of electrons, which heats the material locally to a temperature above the vaporisation temperature of the reaction product —removal step—.