Two examples illustrate the propagation of instability modes under quasi-static, steady-state conditions. The first is the inflation of a long cylindrical party balloon in which a bulge propagates down the length of the balloon. The second is the collapse of a long pipe under external pressure as a result of buckle propagation. In each example, there is a substantial barrier to the initiation of the instability mode. Once initiated, however, the mode will not arrest if the pressure is in excess of the quasi-static, steady-state propagation pressure. It is this critical pressure that is determined in this paper for each of the two examples.

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