In paper fundamental problems of wave dynamic stratified medium modeling (ocean, atmosphere) are considered. The basic mathematical models describing the processes of excitation, the propagation of internal gravity waves in vertical stratified horizontally inhomogeneous and non-stationary medium are presented. The uniform asymptotic forms of the internal gravity waves in horizontally inhomogeneous and non-stationary stratified medium are obtained. A modified spatio-temporal ray method is proposed, which belongs to the class of geometrical optics methods (WKBJ method). Analytical and numerical algorithms of internal gravity wave calculations for the real stratified medium parameters are presented. Some results of internal gravity waves measurements in real stratified medium (ocean, atmosphere) and it’s interpretations are discussed. The universal nature of the developed asymptotic methods of modeling makes it possible to efficiently calculate the wave fields and qualitatively analyze the solutions obtained, which makes it possible to analyze wave patterns in general, to correctly set up mathematical models of wave dynamics, and to carry out express estimates in actual measurements of wave fields in natural stratified medium.