Abstract: Boundary (and initial) conditions choice for the effective generation and propagation of nonlinear sound in a stratified medium is studied. The adjustment to a medium type is introduced via a choice of equations of state. Liquid, liquid with bubbles and gas cases are considered. Model propagation equations are derived for the special cases of plane directed waves. The application of the conditions in two-dimensional version (three-dimensional with the cylindric symmetry) is discussed and some test calculations of solutions are performed numerically. A good shape and direction conservation in a weak nonlinear conditions is discovered for a triangular initial wave from low frequency range.