In order to understand the behavior of shallow structures in dynamic snap-through or buckling, a detailed study has been made for a plane, viscoelastic, three-hinged truss with a concentrated mass at the central hinge, and with a normal load of constant magnitude applied suddenly at this hinge. The dynamic buckling criterion is found to correspond to values of the parameters for which the solution goes into the saddle point of a two-dimensional autonomous system. It is shown that another dynamic buckling criterion, based upon the asymptotic behavior of solutions in time, can give incorrect results in certain cases. Two methods to compute buckling loads are investigated with the aid of a phase plane diagram and potential curves. Approximations to the buckling load, including an upper bound, are computed by means of an energy integral method. The exact buckling loads are computed by numerical integration of the governing differential equation.