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Abrasive flow machining (AFM) is a relatively new process with low material removal ratio for deburring, removing recast layers and finishing industrial components with complex shapes among non-conventional machining processes. In this process, the finishing is handled by flowing of the composition of viscoelastic and abrasive particles on workpiece surface, under the pressure of piston. In this research, the abrasive flow machining process of H13 tool steel with applied an external magnetic field around the workpiece for improve the material removal ratio and surface roughness has been investigated and the effect of magnetic field intensity, abrasive particles mesh and the hardness of workpiece as the input parameters on the process outputs including surface roughness and material removal ratio was studied. Also the regression model of MRR and surface roughness was developed and variance analysis was performed. Results of experiments indicated that increase in abrasive-particles mesh leads to decrease surface roughness and material remove ratio and increase in magnetic field intensity causes to increase material removal ratio and decrease surface roughness. Also the material removal ratio is decreased with increasing of workpiece hardness and on the same condition; better surface finish was achieved in the case of harder workpiece.