Method for producing a base part of a set of artificial teeth, or a set of artificial teeth having a base part, comprising the step of forming the base part by a rapid prototyping process, e.g. 3D lithography and, in particular, 3D laser lithography. Furthermore, the invention relates to a method of establishing a data set representing the shape of a base part of a set of artificial teeth, wherein a gum area or a model thereof is scanned and/or a model of a base part is scanned and/or the shape of the base part is simulated on a computer.