As the use of directed-energy systems (such as intense lasers and high-power microwave devices) continues to increase, the need to better understand the effects of such systems on biological tissues becomes more urgent. In addition to local heating and temperature rise due to energy absorption, the possibility exists for the generation of stress waves that can propagate and potentially adversely affect cellular and sub-cellular structures. One mechanism for generation of stress waves, thermo-mechanical coupling due to thermal expansion, has been discussed in the literature. Another mechanism, direct coupling via the Lorentz-force density, does not appear to have received as much attention. The present study develops closed-form expressions for the stress-wave and displacement fields, as functions of space and time, for the two mechanisms just described. The geometries considered are either half-space, slab, or multilayer with material properties characteristic of relevant tissues like skin, bone, and brain (frequency-dependent permittivity and conductivity curves taken from the literature). The excitation is assumed to be a plane wave at normal incidence. The relative amplitudes and spatial and temporal distributions of the waves are compared and contrasted for a wide band of frequencies (from kHz to GHz). Idealized calculations such as the ones presented in this study should prove useful in determining which mechanisms are the most important for inclusion in more detailed, three-dimensional, coupled multi-physics analyses going forward.