Summary: It is well known in the surface wave theory that the secular equation for surface wave speed \(v\) can be written as \(\det M=0\) in terms of the surface-impedance matrix \(M\). It is shown in this paper that \(M\) satisfies the simple identity \((M-iR) T^{-1}(M+ iR^T)-Q+ \rho v^2I=0\) is the usual notation in Stroh formalism. This identity provides an efficient method for calculating the wave speed of surface waves in unstressed or pre-stressed elastic half-spaces. The method is explained and illustrated by examples. It is also shown that the buckling/wrinkling pre-stress for a pre-stressed elastic half-space can be calculated using the same procedure, but with pre-stress playing the role of \(v\).