Modern technologies of harvesting sugar beet tops provide solid preliminary cutting and collecting its harvest at the increased altitude and subsequent additional root crops heads cleaning from tops residues on a root. This last operation also defines quality of root crops of beet before their digging up. Objective of this research is improvement quality of root crops heads cleaning from tops remains, by development of interaction theory of flexible cleaning blade with a spherical surface of root crop head. In the theoretical study were used methods of modeling, higher mathematics and theoretical mechanics, as well as programming and carrying out numerical calculations on the PC. As a result of the conducted theoretical research the interaction theory of flexible cleaning blade with a root crop head surface in the course of its cleaning from tops remains is developed. On the basis of the received differential equations of blade movement which is pivotally mounted on the drive shaft with a horizontal axis of rotation, new mathematical dependences which justify basic parameters of this technology process are given.