Tapered steel tubes with regular convex polygonal section are widely used in the construction industry, for supporting lighting and telecommunication equipment, as well as overhead power lines. Such tubes are thin-walled and therefore susceptible to cross-section deformation (namely warping, distortion and local buckling), thus their structural analysis invariably requires resorting to refined shell finite element models. In this paper, a new Generalized Beam Theory formulation for such tubes is presented and used to assess the linear, buckling (bifurcation) and vibration behaviour of the tubes. The formulation employs a “parent element” approach to map the element configuration using the deformation modes of the prismatic case. Even though the fundamental equations are significantly involved due to the taper effect, it turns out that it is possible to define the usual Vlasov GBT deformation modes (those complying with the null membrane shear strain assumption), an aspect that is essential for the overall performance of the formulation. In fact, it is also possible to define, analytically, the inextensional deformation patterns for these tubes. For comparison purposes, results obtained with refined shell finite element models are provided, and it is shown that the finite element implementation of the proposed formulation can reproduce the structural behaviour of such tubes with remarkable accuracy, even for significant taper ratios. Finally, the linear, buckling (bifurcation) and vibration behaviours of these tubes are assessed regarding their sensitivity to several geometric parameters, such as the taper ratio, the number of folds and the radius-to-thickness ratio.