The main aim of this paper is to perform first self-consistent numerical computation of the response of stellar atmospheres to the propagation of acoustic waves specified by realistic acoustic wave energy spectra. In the numerical approach, stellar atmospheres are stratified, non-isothermal and plane-parallel, and only their magnetic-free regions are considered. The resulting atmospheric heating is calculated and the time sequence of atmospheric velocities computed by a time-dependent hydrodynamic numerical code is analysed. All computations are done adiabatically and Fourier analysis is used in order to determine the oscillatory properties of stellar atmospheres. The numerical approach is supplemented by an analytical treatment in which three different local acoustic cut-off frequencies are selected from the literature; their values in the stellar atmospheric models are calculated and compared to the numerical results. The theoretical results obtained clearly show that atmospheric oscillations do exist in late-type stars and that their origin and physical properties are similar to those observed in the solar atmosphere. The oscillation frequency of stellar atmospheric oscillations ranges from 7.5 mHz for F5V stars to 16.0 mHz for M0V stars. The relevance of this theoretically predicted range of stellar oscillation in solar-like stars to the recent data obtained by the NASA space mission Kepler is discussed.