Abstract. The authors describe the method of calculating the magnetic forces in the working gap in the case of magnetically abrasive machining of flat surfaces of billets from magnetic materials by the periphery of a circular inductor on permanent magnets. The application of the software package ANSIS Maxwell for the calculation of the magnetic induction method in the working gap and the magnetic forces of the magnetically abrasive powder acting on the grain is shown. As a result of the work, the magnetic induction in the working gap was calculated for magnetically abrasive machining of flat surfaces of billets from magnetic materials by an inducer on permanent magnets. Also, calculations showed the distribution of the magnetic abrasive powder in the working gap, depending on the material of the workpiece being processed. In the case of magnetically abrasive machining of a magnetic workpiece, the powder in the working gap is concentrated in the zones with the greatest density of force lines - under the inductor poles. An analysis is made of the distribution of magnetic forces in the working gap during magnetic abrasive machining.