Abstract: Dynamic stability and dynamic buckling loads of elastic structures have gained numerous interest in recent research. It is because of its wide area of application in many fields of engineering such as civil engineering, architectural engineering and nuclear power plant engineering. Dynamic buckling load of a geometrically imperfect column lying on a nonlinear elastic foundation trapped by a time dependent load is discussed here. Regular perturbation method and asymptotic expansions are applied to solve the differential equation. The effect of damping and geometric imperfections on the dynamic buckling load at different modes are x-rayed.