The susceptibility of axially loaded steel members with angle cross-sections to vibrations depends on their fundamental natural frequency. Design steel standards guard against excessive vibrations by enforcing slenderness limits of 200 for compression members and 300 for tension members. This approach indirectly controls the member’s natural vibration but does not reflect the effect of axial force level within the member, nor the type of connection at the member ends on its susceptibility to excessive vibrations. For members with angle cross-sections, in which the shear centre is offset from the section centroid, the fundamental vibration mode involves a combination of flexure and torsional deformations. The corresponding natural frequency depends on the cross-section geometry, member span, level of axial loading with the member, end connection details, and the eccentricity of the axial relative to gusset plates at both ends of the member. Within this context, the present study presents the results of a parametric study that investigates such effects by conducting a series of natural vibration analyses based on a stressed Eigen-value type of solution, for a spectrum of compressive and tensile members with angle cross-sections. The analyses are based on closed-form solutions and shell finite element models developed in Abaqus. The study presents a step towards proposing refined slenderness limits for axially loaded members.