Anomalous results, including counterintuitive permanent displacements and scatter of numerical solutions, have been found for certain fixed-pin supported beams deformed plastically by a transverse pressure pulse. Similar difficulties may be anticipated in other pulse loaded beams and plates with constraints that prevent in-plane displacements. The present studies show some of the special circumstances in which these occur, with a simple elastic-plastic model of Shanley type. In particular, effects of changing a geometrical ratio and of including damping are shown over a range of load magnitudes. The influence of damping is remarkable. Unpredictability of final displacement is evident in special circumstances, such that the final displacement is hypersensitive to the parameters of the loading, structure and solution technique.