In this paper the influence of section properties on thin walled beam sections with restrained torsion is studied by considering the angle of twisting for non-uniform torsion. The study is based on the governing equation for non-uniform torsion of thin-walled beam of open and closed cross-sections, including the restrained behavior. The hyperbolic shape functions is used to generate the general solution for homogenous equation as it gives the exact results in accordance with the analytical solution. This study is focused on a bar subjected to torsion with warping of wide-ranging open and closed cross-sections with different value of characteristics number for torsion. The impact of the characteristics number for torsion on different section type is studied and evaluated. The obtained results are compared based on the influence of section properties on the components of the total applied torsion and presented graphical for different value of characteristics number for torsion. © Published under licence by IOP Publishing Ltd.