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• Model of tower cranes carrying slender payloads is derived. • Equation for estimating the twisting frequency is presented. • A discontinuous piecewise smoother is proposed for controlling swing and twisting. • Experiments validate dynamic behaviour and the control effectiveness. Tower cranes suspending slender payloads are widely used in the construction site. Both the payload swing and twisting degrade the efficient and safe operation. However, the twisting dynamics is more complicated than the swing dynamics. Although numerical analysis of the twisting dynamics has been reported, little attention has been directed at the analytical analysis of the twisting dynamics. A new dynamic model including swing and twisting has been derived in this article. The analytical analysis of the twisting dynamics from the new model has been described. The closed-form solution for estimating frequencies of the payload twisting have been presented. In addition, a new control method is proposed for suppressing swing and twisting in tower cranes transporting slender payloads. The control method has good robustness to variation in working conditions and system parameters, and good performance in rise time. Numerous simulations and experiments demonstrated the key dynamic behavior of the payload twisting and effectiveness of the control method. [ABSTRACT FROM AUTHOR]