Grooves with nanometer scale dimensions can be fabricated on polymer surfaces by moving the tip of an atomic force microscope (AFM) across the surface at constant velocity and fixed applied force F. The grooves consist of a central trough with pile-ups on either side. These grooves are caused by plastic deformation and provide information about surface mechanical properties. We describe new results on the Kapton polyimide. Groove shapes are measured from AFM images taken with zero applied force. The grooves are sufficiently shallow that image artifacts due to the tip shape are unimportant. The surface yield strength is found to be about 125 MPa, as estimated from the applied force and the width of the smallest groove, and is comparable to the bulk tensile strength of 172 MPa. Grooves with pile-up heights that are large compared with the intrinsic surface roughness are found to have a universal shape when scaled to have the same heights and widths. Continuum mechanics models developed for point indentations are not able to describe the properties of the grooves consistently.