When using complex spatial patterns for transportation, the straight screw conveyors have a series of obvious disadvantages. This paper presents a design of a flexible screw sectional working body that allows increasing the functional and operational characteristics of screw conveyors used in the transportation of bulk agricultural materials. A mathematical model of the dynamic system of a flexible screw conveyor has been established, and dynamic starting torques have been calculated at the rated load of loaded screw, and when the system is braking. Analysis of the results obtained shows that, with significant damping coefficients, the start-up transition process occurs smoothly, and the load reaches its rated value without torque and speed fluctuations. It has been established that fast braking significantly increases the dynamic loads that may exceed the maximum critical torque of the electric motor (by 50–70% on average) and the rated load torque (by 2.5–3 times).