Analytical solutions for the vibration of a beam with axial force subjected to generalized support motion are obtained in this paper. The finite element method (FEM) is introduced to validate the analytical solution obtained by an analytical approach. The dynamic responses of clamped–clamped, pinned–pinned and clamped–pinned beams with axial tension or compression are obtained via analytical approach and FEM. Comparing results show that the analytical approach is effective. The analytical analysis shows that the resonance will occur in general when the oscillatory frequency of transverse motion or rotation of any support end is equal to the natural frequency of the beam. Moreover, several cases in which the resonance disappears even if the frequencies of support excitations are equal to the natural frequencies of the beam are detected and are validated by the FEM solution.