The possibility of amplification of acoustic waves in inhomogeneous atomic dc gas-discharge plasma (positive column of glow discharge) is investigated theoretically. This amplification is caused by the transfer of thermal energy from electrons to colder electron gas under conditions of elastic electron-atom collisions. It is demonstrated that the inclusion of nonuniform distribution of equilibrium temperature, neutral gas concentration, and electron concentration over the plasma column cross section, similar to the case of uniform distribution, cannot result in acoustic instability and, consequently, in the interpretation of the experimental results in sound amplification in weakly ionized plasma. The dispersion equation for sound waves in inhomogeneous glow-discharge plasma is derived and numerically analyzed in detail. Comparison of the theoretical and experimental results enables one to identify the reasons for their discrepancy and to actually reveal the basic principles essential for constructing a theory which will make it possible to quantitatively and adequately describe the experimental data on the amplification of sound in weakly ionized atomic plasma.