The initial definitions are presented in the framework of general pressure-coordinate equations of atmospheric dynamics, which incorporates all the spectrum of motions from the planetary scale flow to the local turbulence and acoustical wave propagation. The main continuity and metric qualities of pressure coordinate space are discussed in this general case. Then, the simplifications are introduced, which eliminate the internal and external acoustical waves from dynamics and turn the general equations into an anelastic, nonhydrostatic model in the pressure coordinate presentation. The changes in continuous and metric qualities of the model are traced. Much attention is paid to the elimination of the external acoustical (Lamb) mode and accompanying modification of the surface pressure treatment. The surface pressure becomes adjusted (acoustically relaxed) and subject to evaluation from a diagnostical relationship. The model includes only three prognostic equations - for temperature and horizontal wind components. Temperature equation coincides with the hydrostatic case, while the wind tendency equations include additional forces, which take into consideration the nonhydrostatic and the surface pressure adjustment effects.