Beet tops harvesting is a complex task of the sugar beet growing industry which forms the qualitative indicators of root crops during their further digging out from the soil and determines the loss of tops and sugar-bearing mass. In the development of theoretical foundations of the optimal tops cutting from heads of sugar beet root by different types of topping working bodies should take into account forces which act at the same time and the rational cutting height. Theoretical researches having been carried out hitherto concerned only the detailed analytical description of the functioning of the new designs of topping working bodies and practically did not concern the general provisions of the separation tops from the head of root crop. The aim of this study is the theoretical determination of the forces that occur at the contact point of cutting working body of topper machines with root crops head of sugar beet root crop. When carrying out theoretical studies are used the methods of mathematics, theoretical mechanics, strength of materials, methods of programming and numerical calculations on PC. As a result, of the theoretical research new analytical dependencies of force describing the processes of crumpling and subsequently cutting of sugar beet heads by topping working body, depending on the size and shape of root crops heads and design parameters of topper have been obtained. As a result, of numerical calculations on PC critical level value of penetration of the cutting element of topping working body into root crops head of sugar beet and maximum value of cutting force at which ejection of root vegetables from the soil doesn’t take place, was defined. The obtained theoretical dependencies and values of normal reaction and cutting forces are the basis for the further working out of a mathematical model of dynamic interaction system of cutting working bodies with the heads of sugar beet.