With the distributed transfer function method, a closed-form solution is obtained for free vibration and stability of a multiple-step beam under stepped axial pressures. According to variations of the geometry of the cross-section, the material and the axial pressure in axial direction, the beam is divided into multiple sub-beams whose closed-form solution is obtained with the distributed transfer function method. The natural frequencies and buckling loads along with their mode shapes are obtained by using the displacement continuity conditions and force balance conditions between the sub-beams. The method was validated through numerical examples of three-step beams. The natural frequencies of multiple-step beams under different axial pressure in each section were calculated with the example of four-step beams.