Abstract <p>For an incompressible stratified elastic strip, a Poincaré–Steklov operator mapping normal stresses to normal displacements on part of the strip boundary is considered. The transfer function (TF) of the operator is constructed using a variational boundary value problem for displacement transforms. A weak solution of the variational problem is defined, and its existence and uniqueness are proved. The problem is approximated using the finite element method. The leading term of an asymptotic expansion of the TF is obtained for small values of the Fourier transform parameter, and a three-term asymptotic expansion of the TF is derived for large values of the Fourier transform parameter. Padé approximants of the resulting asymptotic series are constructed. A combined approach reducing computational costs is developed for the computation of the TF based on its asymptotic expansions and Padé approximants.</p>