This paper presents a geometrically exact (in the sense of Simo, 1985) two-node spatial beam finite element for thin-walled I-section members with web and flange tapering. The element formulation is derived directly from the three-dimensional continuum by introducing standard thin-walled beam theory kinematic assumptions, and hence the peculiar effects due to the tapered geometry are correctly modelled. The torsion-related warping function is derived directly for the tapered geometry, the element accurately captures the inclination of the stress and strain fields in the inclined flanges, load eccentricity effects, including loads applied away from the centroid and shear centre, as well as Wagner-torsion effects. A complete and compact matrix-vector formulation is provided for the computational implementation of the element. The performance of the formulation is assessed through several numerical examples, demonstrating its accuracy and computational efficiency in linear, linear stability (calculation of bifurcation loads and buckling modes), and large-displacement path-following analyses. Comparisons with reference solutions from the literature or with results obtained using refined shell finite element models show excellent agreement, confirming the high accuracy of the proposed element. For illustrative purposes, the figure displays a comparison between the proposed beam element (15 elements) and a refined shell finite element model, for a slender beam subjected to biaxial bending and torsion. The graph displays the evolution of the displacement of the loaded point with the load parameter λ, showing an excellent match. Simo, J. (1985) “A finite strain beam formulation. The three-dimensional dynamic problem. Part I.” Computer Methods in Applied Mechanics and Engineering, 49(1), 55-70.