resting on an elastic foundation of constant yL/7r*EL = 4.5. Table 1 shows a comparison of the first and second mode shapes of vibration and static buckling. The resulting regions of instability for the first two end conditions are shown in Figs. 3 and 4. The various degrees of similarity between the modes are reflected in the widening or narrowing of the regions. For the third end condition, the similarity in the mode shapes is pronounced. The regions for this case are very close to Fig. 2. Finally, for the pinned-pinned condition, the dissimilarity between the respective modes of the same order is evident. However, because of the definite similarity between the first and second modes of vibration and buckling, if the vertical ordinate is normalized with respect to the Pi* and the coordinate with respect to co2, Fig. 2 will be obtained. In conclusion, the dissimilarity in the mode shapes tend to stabilize the bar dynamically.