Oscillating rasps for the surgical preparation of the bone prior to the implantation of a glenoid or acetabular component with complex geometry are disclosed. Surgical methods for the use of such oscillating rasps are also disclosed. The oscillating rasp includes an attachment head configured to be secured in a chuck of an oscillating tool, and a cutting head secured to the attachment head. The cutting head includes a cutting surface extending posteriorly from the longitudinal axis of the oscillating surgical rasp. The cutting surface has a plurality of cutting teeth arranged in a geometry that, when oscillated along a predetermined path in contact with the glenoid of the patient, corresponds with the geometry of the augmented glenoid prosthesis.