During the interaction of a laser pulse with the surface of a solid object, the object always gains momentum. The delivered force impulse is manifested as propulsion. Initially, the motion of the object is composed of elastic waves that carry and redistribute the acquired momentum as they propagate and reflect within the solid. Even though only ablation- and light-pressure-induced mechanical waves are involved in propulsion, they are always accompanied by the ubiquitous thermoelastic waves. This paper describes 1D elastodynamics of pulsed optical manipulation and presents two diametrical experimental observations of elastic waves generated in the confined ablation and in the radiation pressure regime.