AbstractIn this study, the three parameters of the abrasive particle size, distance of tool to the work piece, and the rotational speed of cylindrical surface finishing of steel AISI 321 by abrasive particles in the MAF magnetic field was studied. The advantages of this process that can be noted are the lack of residual stress after the process and modification of the coaxial shaft. Surface roughness was considered as a function of rotational speed (RPM), the distance between tool and work piece (GAP) and the size of the abrasive particles.Special tools for finishing the cylindrical surface (shaft) are designed from mentioned material and the rotational motion of the shaft is provided by the lathe. Experiments were performed according to full factorial method, using abrasive powders consisting of a mixture of silicon carbide SiC with carbonyl iron Fe in different particle size and SAE40 oil. After the surface roughness measurement of samples, the influence of various parameters on the final surface quality was evaluated, the results have shown that in the mentioned stainless steel shaft finishing, variables of 1. Distance between tool and work piece 2.Abrasive particle size 3. Rotation speed, respectively, have the highest influence on obtained surface roughness. Finally, by using the neural network analysis, a better condition in terms of three parameters was obtained to achieve better surface finish.