Abstract: This paper studies the inherent vibration of steel structures with the flexural member supported by a compression member by the method of Laplace transformation and singular functions. The modal functions of the compression member and the flexural member are derived, and the characteristic equation for inherent vibration frequencies of a steel structure with the flexural member supported by a compression member is obtained by the continuous conditions of supporting. It is shown that its inherent vibration frequency increases with the axial pressure.