The axial impact by an elastic body on an elastic-rod end with a fixed opposite end is considered. The propagation of elastic waves in the rod and the local deformations in the contact zone are taken into account. After recoil of the body, the rod performs free longitudinal vibrations, which can under certain conditions cause parametric transverse vibrations having the character of beats. Depending on the parameters of the problem, the collision time, the shock-pulse shape, and the greatest amplitude of the transverse vibrations under parametric resonance are determined.