The interaction between tillage tools and soil is of a primary interest to the design and use of these tools for soil manipulation. A new explicit mathematical model to calculate the angle of soil failure plane when soil is cut with narrow tine was developed. Equations of Soil cohesion and soil adhesion cutting factors were partially differentiated with respect to angle of soil external friction, were maximized; Values of angle of soil failure plane were calculated by the model for tine rake angle range from 00 to 900 operated at 0.3 m depth and 0.15 m width in soils with different mechanical properties. It was found that angle of soil failure plane is acute and its values were used for calculating soil frictional cutting factor, soil overburden cutting factor, soil cohesion cutting factor, soil adhesion cutting factor, rupture distance, width of side crescent and soil resistance force. It was found that the force values were realistic. Therefore, the model is valid.
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