Method for forming the tooth shape of a first and a second annular gear of an annular gear machine, comprising the following steps: a) establishing a starting geometry of the first annular gear, being an outer ring of the annular gear machine, at least one quality criterion of the annular gear machine as well as a desired eccentricity (e) between the rotation axes (A, B) of the two annular gears, wherein the starting geometry is described by high-order splines; b) performing a movement with the starting geometry established, wherein the starting geometry performs a rotational movement about its own rotational axis and at the same time a revolving movement about the rotational axis of the second annular gear, and wherein this rotational movement and this revolving movement are interrelated such that the angle of rotation (b) of the eccentricity (e) is continuously equal to the product of the angle of rotation (a) of the first annular gear and the number of teeth of the first annular gear (b = a × Z); c) generating the tooth shape contour of the second annular gear by plotting the path described by the envelope curve of the starting geometry when performing the movement according to step b), wherein the plotted tooth shape contour is described by high-order splines; d) checking for the quality criterion to be fulfilled with the starting geometry and the plotted tooth shape contour; e) if the quality criterion is not yet fulfilled, varying the previously used starting geometry and/or the established eccentricity (e); f) iterative repeating of steps b) to e) and generating a different tooth shape contour until the quality criterion is fulfilled. a) establishing a starting geometry of the first annular gear, being an outer ring of the annular gear machine, at least one quality criterion of the annular gear machine as well as a desired eccentricity (e) between the rotation axes (A, B) of the two annular gears, wherein the starting geometry is described by high-order splines; b) performing a movement with the starting geometry established, wherein the starting geometry performs a rotational movement about its own rotational axis and at the same time a revolving movement about the rotational axis of the second annular gear, and wherein this rotational movement and this revolving movement are interrelated such that the angle of rotation (b) of the eccentricity (e) is continuously equal to the product of the angle of rotation (a) of the first annular gear and the number of teeth of the first annular gear (b = a × Z); c) generating the tooth shape contour of the second annular gear by plotting the path described by the envelope curve of the starting geometry when performing the movement according to step b), wherein the plotted tooth shape contour is described by high-order splines; d) checking for the quality criterion to be fulfilled with the starting geometry and the plotted tooth shape contour; e) if the quality criterion is not yet fulfilled, varying the previously used starting geometry and/or the established eccentricity (e); f) iterative repeating of steps b) to e) and generating a different tooth shape contour until the quality criterion is fulfilled.