Abstract: A method and a grinding machine for centerless angular plunge grinding a workpiece are disclosed. The workpiece is rotatable about a first axis and has essentially cylindrical sections of different diameter and at least one shoulder located between the sections. The grinding wheel has a conically shaped periphery and is rotated about its axis inclined relative to the workpiece axis by a predetermined angle. The grinding wheel is brought into engagement with the workpiece with at least an axial surface line of its periphery. The grinding wheel and the workpiece are fed-in relative to one another by a predetermined amount of overmeasure. The feeding-in is effected in at least two steps. In a first step the feeding-in is effected essentially in a radial direction. In a second step the feeding-in is effected essentially in an axial direction. In the first step essentially the overmeasure in the area of the cylindrical sections is removed. In the second step essentially the overmeasure of the shoulder is removed.