A comparatively simple method of analysis is developed to determine the deformations in a beam subjected to lateral impact of such a magnitude that plastic strains large compared with elastic strains occur. A useful approximation to the motion then can be obtained by neglecting elastic strains and considering rigid-body motion of segments of the beam joined at plastic hinges where the entire deformation takes place. A method of analyzing such a situation is described and applied to a beam subjected to central impact. The approximate final permanent deformation is obtained; this includes deformation during application of the load, and plastic flow which continues afterward when the kinetic energy of the motion generated by the impact is transformed into additional plastic deformation. A criterion is given for conditions when this type of theory can be expected to provide a satisfactory analysis. The method of solution provides an interesting analogy to the concept of static determinacy which has been used in the analysis of quasi-static plastic-flow problems.