The authors study the stability of an elastic column driven by a fluctuating load. They consider a sequence of approximations to the continuous column by first, a simple pendulum with an impulsive random force applied at the hinge, then by a double pendulum and finally, by an N-fold pendulum with a vertical or tangential random load. They find a stability criterion which depends on the noise to damping ratio. Even if the fluctuating load is sub-critical on the average, they show that the structure may not be stable, and its energy may reach any level. In this case they calculate the mean time to reach a given energy level and use this time as an index of reliability of the structure. The authors consider both the vertically loaded column (the Euler column) and the tangentially loaded column (follower load). Two types of noise are considered, a random impulsive force and Gaussian white noise. In either case the qualitative behavior of the pendulum or the column is the same.