A comprehensive analytical solution is developed to generate the interaction functions of a rigid permeable strip in contact with a saturated porous elastic half-space. Linear hysteretic damping characteristics of the medium are included in the formulation. The mixed boundary-value problem of a welded (and smooth) surface footing is reduced to a set of coupled Fredholm integral equations of the first kind and a numerical solution is provided. Frequency-dependent interaction functions (stiffnesses and radiation damping coefficients) of a medium modelling a saturated dense sand are computed and exhibited graphically to reveal the influence of pore water, permeability effects and hysteretic damping characteristics of the medium. In the horizontal mode of response and without hysteretic damping, the pore water causes the effective stiffness to increase by 50–100% while it has negligible influence on the damping coefficient. With 5% hysteretic damping, the horizontal stillness changes sign and character and there is an increase of about 25% in its magnitude compared to the corresponding dry case. For the vertical and rocking modes of response, the impact of pore water on the interaction functions (both stiffnesses and damping coefficients) is much more pronounced. Without hysteretic damping, there are changes in sign in the stiffnesses of the medium, and the magnitudes of the interaction functions, relative to the corresponding dry case, could be as large as several folds, especially for the higher values of the dimensionless frequency. At 5% damping, the effective stiffnesses are increased by about 25–50% while the damping coefficients almost double. Concerning the influence of types of contact, the interaction functions are practically identical for smooth and welded contacts over the frequency range of interest. The results are useful in determining the response of surface structures to seismic excitation, in particular, where the ground water is at a level to impact such response.