We study lateral vibration of a simply supported axially compressed elastic rod with rotary inertia. The axial force is assumed to be a function of time. Stability of the solution is examined. The conditions are examined under which the temporal evolution of the system is a slowly varying and regularly slowly varying function. Also some properties of the generalized solution to the problem are examined. Our results on stability boundary obtained by dynamic, method agree with the results obtained by static (Euler) method.