Summary A dimensionless number, termed response number in the present paper, is suggested for the dynamic plastic response of beams and plates made of rigid-perfectly plastic materials subjected to dynamic loading. It is obtained at dimensional reduction of the basic governing equations of beams and plates. The number is de®ned as the product of the Johnson's damage number and the square of the half of the slenderness ratio for a beam; the product of the damage number and the square of the half of the aspect ratio for a plate or membrane loaded dynamically. Response number can also be considered as the ratio of the inertia force at the impulsive loading to the plastic limit load of the structure. Three aspects are re¯ected in this dimensionless number: the inertia of the applied dynamic loading, the resistance ability of the material to the deformation caused by the loading and the geometrical in¯uence of the structure on the dynamic response. For an impulsively loaded beam or plate, the ®nal dimensionless de¯ection is solely dependent upon the response number. When the secondary effects of ®nite de¯ections, strain-rate sensitivity or transverse shear are taken into account, the response number is as useful as in the case of simple bending theory. Finally, the number is not only suitable to idealized dynamic loads but also applicable to dynamic loads of general shape. where r and V denote stress and particle velocity, respectively. To make it dimensionless, we introduce the dimensionless variables as follows: