In this study, the free vibration analysis of cylindrical and non-cylindrical helicoidal bars with thin-walled circular tube cross-section is investigated by using the mixed finite element formulation based on Timoshenko beam theory. Frenet triad is adopted as the local coordinate system in the helix geometry. The curved elements involve two nodes, where each node has 12 DOF, namely three translations, three rotations, two shear forces, one axial force, two bending moment and one torque. Numerical solutions are performed to analyze the dynamic behavior of the helix geometries and benchmark results are presented. Parametric studies are carried out to investigate the influence of the section geometry, the helicoidal geometry, the boundary conditions and the density of the material.