Grinding wheel

A semi-permanent peripheral grinding wheel comprising ultrahard abrasives such as diamond or cubic boron nitride is provided which overcomes the serious problems caused by "chatter". The wheel comprises a hub mounting the ultrahard abrasive, the abrasive being resiliently depressible radially inwardly of the wheel. The wheel preferably has a radial static stiffness of no more than 1.5x106 N/m per mm. of wheel width and a first radial natural frequency of at least 500 Hertz. The resiliency may be provided by rubber pads between the abrasive and the hub, or by mounting the abrasive on a hub made of resiliently deformable metal such as "RETIMET" (Registered Trade Mark) sponge-like metal.