Small oscillations of a beam-column with finite electrical conductivity in a transverse magnetic field are examined under the assumption that the vibration of the bar causes only a weak perturbation in the electromagnetic-field. The frequency equation is derived for a column and reduced to that for free vibration of a beam by equating the end load to zero. The roots of this equation are obtained approximately and the effect of the magnetic field on the frequencies is noted. In addition, the elastic stability of a conducting column and beam-column are investigated. The effect of the magnetic field on the buckling load is determined. Numerical results are presented which indicate that the effect of the dynamic electromagnetic forces is negligible except at extremely high frequencies of vibration.