We consider axially-compressed thin cylindrical shells, which deform e
lasto-visco-plastically under high intensity external impulsive loadin
g and in which volume damage can occur. The shell carrying capacity is
determined in accordance with deformation, stability and strength cri
teria. Our purpose is, introducing special dimensionless parameters, t
o obtain the relation between the geometrical sizes and the material c
haracteristics of the shell - on one hand and the dynamic impulse para
meters (amplitude and duration) on the other, when the shells lose the
ir carrying capacity.