An acetabular rim cutter has an annular cutting face provided on a rotatable carrier. A coupler is provided for attaching the carrier to a rotational power source. A guide element is axially aligned with the cutting face to locate and align the cutting face on the acetabulum with which it is to be used. Preferably, the guide element is axially movable in relation to the cutting face and a resilient element is provided for biasing it axially away therefrom.