AbstractRadial and tangential grinding forces were presented as four components connected with workpiece material microcutting and plastic deformation, and friction of cutting and abrasive grains (AGs) with the workpiece.The depth of abrasive grain penetration in the workpiece and the cutting width are determined with regard to ultrasonic vibrations (USV) amplitude and frequency. Summing up of the forces from single grains was conducted by using a multiple integral, provided that one of the integration limits is a function describing change of the depth of the AGs penetration in the workpiece material which depends on the USV parameters. Dependencies were obtained for calculation of all grinding force components at different vibration amplitudes and frequencies when various number of USV waves fits the contact arc of the grain and the workpiece.Experimental values of grinding forces turned out to be 10 – 15% lower than those when USV waves are not applied.