A mathematical model of loading of the nose-free cutting edges of each insert of the face mill with a spiral-stepped cutting scheme was created. It was established that the size of the cut elements depends on the feed magnitude, the design parameters of the mill and the position of inserts on the contact arc. Variable factors of simulation included the feed magnitude, the clearance angle of the inserts and slope angles of the cutter assemblies. This made it possible to determine the chip thickness and width of cut, the depth of cut, the maximum value of the main cutting edge angle and the cut area at an arbitrary position of the face mill on the contact arc. Simulation in the SolidWorks Motion environment has confirmed reliability of mathematical modeling of loading of the cutting edges of the mill. The relative error in determination of the cut area was in the range from 1.8 % to 5.7 %. Calculation of the cut elements in the arbitrary position of the cutter insert on the contact arc was made in the Maple environment. Analysis of influence of the design parameters of the cutter and the magnitude of feed on the values of the cut elements was made. It has been established that an increase in feed caused a linear increase in the chip thickness and width of cut and the depth of cut for the inserts of all steps. Optimal values of the clearance angle of the mill inserts (16°) and slope of the cutting assemblies (6°) were determined for the milling depth of 3 mm. Recommendations on the choice of rational values of design parameters of the face mill for its effective operation at various depths of cut were given. Thus, there are grounds to assert the possibility of improving productivity of machining flat surfaces at a required quality due to the use of nose-free face mills with a spiral-stepped cutting scheme.