For beams with elastic supports, influence of the spring stiffness on parametric stability boundary of an axially excited beam is presented for the first time. Here, based on Hamilton , s principle, dynamic governing equation of the axially excited beam supported by linear springs on both sides is established. The natural frequen?cies of the beam with axial compression are calculated by the analytical method. The relationships between the stiffness of the supporting spring, the natural frequencies and the critical loading of the system are obtained. Based on Galerkin truncation, semi-analytical and numerical solutions of the steady-state response are obtained by the multi-scale method and the Runge-Kutta method. The effects of the excitation amplitude, supporting stiffness and the average axial force on the nonlinear response are discussed. The stability boundary of the parametric resonance is obtained by the Routh-Hurwitz stability criterion. The influence of the supporting stiffness and the damping on the stability of the parametric resonance are fully discussed. It is found that the stiffness of the supporting spring can significantly change the parametric stability boundary of the beam. Therefore, the results will provide guidelines for design of structures subjected to axial excitation.