THE CLASSIC THEORY of elastic buckling is based on the equilibrium of external and internal bending moments. It does not consider, however, the time elements and the inertia forces involved. The lateral vibration of compressed bars has been investigated, but the use of formulas so obtained for the experimental determination of elastic buckling loads apparently has not been widespread. Yet, this method has many promising aspects. Little information seems to be available on buckling under impact, although this problem must confront many engineers. In this article, time-deflection relations are investigated when an axial force is rapidly applied to a nearly straight bar. Distinction is made between two cases: In the first, the force applied is smaller than Euler's load for elastic buckling; in the second, it is greater. The investigation is limited to cases where the center deflection of compressed bars stays relatively small with respect to the length of the bars. The curvature of the elastic line is therefore assumed to be proportional to the bending moment, independent of the slope, A rigorous analysis, using the strict equation for the curvature and considering inertia forces, would become unduly complicated. However, calculations show that a center deflection of 11 per cent of the original hinge distance increases the elastic buckling force by only 1.5 per cent, while the hinge distance is decreased by 3 per cent. The method of analysis set forth here should therefore cover the large majority of practical cases. Damping is not considered in this analysis. However, where it is of importance and the damping constants can be established, a correction factor for damping can readily be applied to the respective equations.