The single degree of freedom numerical model of plain milling in time domain is represented in this article. This model allows to take into account the process damping phenomena, which is caused by contact interaction along the cutting edge flank face, on the dynamic behavior of the compliant technological system. The particular feature of this research is the usage of the iterative procedure to make more accurate the solutions on each time step of the modeling, which ensures the fulfillment of stiffness equations in the formula for the contact interaction forces calculation along the cutting edge flank face. The analysis of results, which were obtained using the represented milling dynamics model, shows that the process damping may have a significant influence on the technological system dynamics when machining on the modes with low value of the cutting tooth pass frequency ratio to the natural frequency of the system. The proposed methodology of the contact interaction forces calculation along the flank face of the cutting edge may be developed later on for the 3D multiaxial machining of figurine-shaped workpiece.