A theory was developed in [1] for the dynamical behaviour under transverse load of ideal fibre-reinforced beams (that is, beams which are inextensible in their longitudinal direction) which exhibit rigid-plastic mechanical response. This theory is here applied to the problem of a beam of finite length, free at both ends, which is struck centrally by a mass which subsequently adheres to the beam. The general solution for the motion of the beam is determined for a fairly wide class of non-linear strain-hardening laws. Simplified approximate solutions are derived for the cases of (a) a heavy striker, (b) a light striker and (c) low impact speed and/or slight strain-hardening.