It is shown that hydrodynamic phenomena in the chromospheric portion of the flaring solar atmosphere depend dramatically on whether chromospheric evaporation by thick-target fast-electron heating is "gentle" or "explosive." In the case of gentle evaporation, velocities in the upper chromosphere are upward. In the case of explosive evaporation, the overpressure of the evaporated material drives downward motion in the residual flare chromosphere. The plasma driven downward by explosive evaporation is cool and dense in comparison with the chromospheric material ahead of it. We review previous discussions of these "chromospheric condensations" and conclude that physical understanding has been incomplete. We suggest that these condensations are an inevitable consequence of compression of a thermally stable heated plasma. We then investigate the nature of hydrodynamic waves in a heated, strongly radiating, optically thin plasma. It is first shown that acoustic waves in the flare chromosphere travel more slowly than adiabatic or even isothermal sound waves. Next, a simple model for the formation and propagation of chromospheric condensations is developed. This model is based on the propagation of a compression wave into the chromosphere, with quasi-steady equilibrium between flare heating and radiative losses on each side of the compression front. We derive jump conditions and accretion rates for the compression wave. We find that this simple model agrees well with our numerical simulations.