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High strength combined with minimum weight is a distinctive feature of thin-walled beams of open cross-section. A high degree of material economy can be achieved by using non-uniform members of this type. This is the salient feature of thin-walled structural members of open sections such as H, Z, T channel and angle sections. Tapered thin-walled members of open sections are frequently employed for their structural efficiency. In the present analysis torsional behaviour of steel tapered cantilever beam subjected to time-invariant axial compressive load is investigated. To infer its torsional behaviour, secondary effects such as rotary inertia and effect of warping have been taken into consideration. In this work frequency analysis of thin-walled tapered I-sections is carried out to obtain the natural frequencies and corresponding mode shapes. The numerical solutions are obtained from finite element method.