A computational approach is proposed for the mechanical analysis of the multifilament twisted yarn based on the Finite Element Method (FEM). The physical and the geometrical properties of the filaments and the ideal yarn geometrical structure are considered for the mechanical modelling. The tensile and bending deformations of yarns are simulated for the prediction of the respective properties and the computation of the deformed shape. Considerable complexity appears in the mechanical analysis of fibre assemblies, including the structural multiformity, the material nonlinearity and the large deformation effects occurring. The FEM applying the beam theory enhanced with advanced solution algorithms approved appropriate for the analysis. Besides the comparison to an existing analytical model, a set of experimental data derived from 2- to 1200-filament twisted yarns is used for the evaluation of the accuracy of the proposed approach. The effect of the major structural parameters as the filament radius and the yarn twist in the elastic properties and the bending rigidity is also examined.