This paper investigates methods for reaction loads extraction in floating offshore wind turbines (FOWTs) within the modal-based aeroelastic modeling framework. Three methods belonging to two different principles (internal and external loads) are presented, where the two external load principle-based methods ('AuxDOFs' and 'd'Alembert') are rigorously developed for extracting 6-dimensional reactions loads at different cross sections. Verification and evaluation of the developed methods are performed using three different structural systems, as well as comparison with FAST. It is shown that 'AuxDOFs' and 'd'Alembert' methods are preferred over the internal load method due to the significantly improved accuracy and the ability to extract reactions in rigid substructures. Finally, the developed methods are applied to evaluate the influence of tower torsional degree of freedom (DOF) on FOWT loads for four different types of foundations, considering different load cases. Extensive simulation results indicate that neglecting the tower torsional DOF in the modal-based simulation tools can lead to underestimation of FOWT loads. • Reaction loads of FOWTs extracted using internal or external load-based principle. • The 'AuxDOFs' method facilitates reaction loads extraction at critical locations. • The 'd'Alembert' method enables extracting reaction loads at an arbitrary location. • The idling case exhibit the largest difference when including tower torsional DOF. • Neglecting tower torsional DOF in modal-based tools lead to underestimation of loads. [ABSTRACT FROM AUTHOR]