The authors present a new approach for analyzing the elastic wave propagation in layered media. As is known, the Navier harmonic vector equation can be expressed in terms of two quantities: \(e=\nabla\cdot u\) (here \(\nabla\cdot\) means the div), and \(\omega=\nabla\times u\) (here \(\nabla\times\) means the rot), with \(u\) being the displacement, \(e\) being the dilation, and \(\omega\) being the mathematical rotation. If the medium is homogeneous, \(\rho\) (density) is constant, and \(e\) and \(\omega\) obey two uncoupled equations, otherwise the two equations are coupled. The idea of the paper is to introduce a new displacement \(U\) through \(u=T(\rho)U\), where \(T\) is an adequate function, and two new objects: \(E=\nabla\cdot U\) and \(\Omega= \nabla\times U\). If \(T\) is subjected to some adequately chosen conditions, the equations for \(E\) and in \(\Omega\) can be split, given two fields, pseudo-dilational and pseudo-rotational. It is shown that in order to obtain such a situation, \(\rho\) must have the form \(\rho=[a_1+ a_2z+a_3 z^2]^{-1}\), where \(z\) is the depth. The authors obtain closed-form solutions for \(E\) and \(\Omega\) in some interesting practical applications, and calculate the Green function in the frequency domain. To obtain the time-domain solution, the fast Fourier transform is used, and several numerical results are presented.