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Problems concerning the stability of shells under dynamic loads can be divided into two classes with regard to the character of the nonsteady motion of the shell. The first class includes problems involving the snap-through of shells. Here, loss of static stability is characterized by a transition through a limiting point on the loading curve. Most investigations of this class of problems have focused on shallow circular shells, circular in plan, which are subjected to an instantaneously applied external pressure of infinite duration [9]. It has been shown [9] that with a smooth increase in the loading parameter, the latter has a value at which there is a sharp increase in the amplitudes of the displacement functions. The studies [6,8] took into account a hole which does not disturb the axial symmetry of the structure, while [4, i0] examined shallow shells with double curvature which are rectangular in plan.