Classical Thomson‐Haskell methods are proven applicable to the asymptotic wave solution in a stratified elastic medium which has both first and second order discontinuities in ρ, λ, and μ. This proof removes a weakness of the original method, which made it unsatisfactory for modeling velocity gradient anomalies. The generalized method, simple in application for a stack of inhomogeneous layers, is used here to derive P-SV reflection/conversion/transmission properties for a transition region in which ρ, [Formula: see text], and [Formula: see text] vary linearly. Although the solution method is approximate, its accuracy is confirmed by comparison with exact solutions.