The formulation of a finite element model for studying the torsion of estraight beams with I-cross section is presented. The isoparametric beam model with rectangular cross sections which do not have deformation in the section plane or out of it, is extended to accommodate the warping of complex cross sections submitted to torsion loadings. The deformation field of the cross section is represented by generalized degrees of freedom and modifications in the original beam geometric compatibility relations were performed to accommodate shear deformations due to section rotation. The compatibility conditions at fixed end and between two connected elements due to the flange bending are assured using a penalty technique to the longitudinal rotation degrees of freedom at the nodal point. The proposed numerical model is implemented and some sample analyses demonstrate its capabilities on the representation of the problem of linear torsion of straight beams with different cross section shapes; e.g, triangular equilateral, elliptic, rectangular, I – symmetric and non symmetric and T section.